How To Check Solutions In System Of Linear Equations By Elimination?

2025-07-20 07:28:37 117

3 Answers

Simone
Simone
2025-07-21 22:41:02
Elimination is one of my favorite methods for solving systems of linear equations because it feels like a game of strategy. The key is to manipulate the equations so that adding or subtracting them eliminates one variable. Let's say you have the system:

3x + 2y = 8
x - y = 1

First, you might notice that if you multiply the second equation by 2, the y terms will have opposite coefficients. So, the second equation becomes 2x - 2y = 2. Now, add this to the first equation: 3x + 2y + 2x - 2y = 8 + 2. The y terms cancel, leaving 5x = 10, so x = 2. Substitute x back into the second original equation to find y: 2 - y = 1, so y = 1.

Sometimes, you need to multiply both equations to align the coefficients. For example, with 4x + 5y = 14 and 3x + 2y = 5, you could multiply the first by 3 and the second by 4 to make the x coefficients 12. Then subtract one from the other to eliminate x. The process is methodical, and checking your solution by plugging the values back into both equations ensures accuracy.
Mic
Mic
2025-07-22 18:06:04
I remember learning this method in class, and it's actually pretty straightforward once you get the hang of it. The elimination method is about getting rid of one variable so you can solve for the other. You start by writing both equations clearly. Then, you adjust them so one of the variables cancels out when you add or subtract the equations. For example, if you have 2x + 3y = 5 and 4x + 6y = 10, you can multiply the first equation by 2 to match the coefficients of x. Then subtract the first from the second, and the x terms cancel out, leaving you with an equation in y. Solve for y, then plug that back into one of the original equations to find x. It's like solving a puzzle where you remove pieces step by step until the picture becomes clear.
Jude
Jude
2025-07-26 10:46:42
When I first tackled elimination, it seemed a bit intimidating, but practice made it click. The goal is to combine the equations to remove one variable. Start by aligning the equations vertically. Look for coefficients that are opposites or can be made opposites by multiplication. For instance, with x + y = 5 and 2x - y = 4, the y terms are +y and -y, so adding the equations cancels y, giving 3x = 9. Solve for x, then substitute into the first equation to find y.

If the coefficients don't cancel directly, multiply one or both equations to create matching or opposite coefficients. For example, with 2x + 3y = 7 and 5x + 4y = 14, you might multiply the first by 5 and the second by 2 to match the x coefficients at 10. Then subtract to eliminate x and solve for y. Always verify your solution by substituting back into both original equations to ensure they hold true.
View All Answers
Scan code to download App

Related Books

Astrophysical Equations of Love
Astrophysical Equations of Love
Nikki Crowman enters a world of mystery and passion at Moonward University, where ambition and intellect collide. Surrounded by the brilliance of her peers, she finds herself drawn to the enigmatic Tom Thorn, the formidable Astrophysics Professor whose icy facade conceals a warmth hidden underneath. As their unconventional romance blossoms, Nikki must confront her past demons to embrace a love she never thought possible. Explore the complexities of love and overcoming trauma in this captivating tale of letting go for the sake of love.
Not enough ratings
15 Chapters
Check Mate
Check Mate
"The game of chess is not just any old board game but it is also the game of life. You can be represented as the king, all the others are the people around you. Check mate means game over in the game but check mate in real life means your life has come to an end..." BORING! Chess is the worst board game on earth, if you're gonna play chess, I'll consider you as one of those who exist and don't live. Chess is the game plan. I play in the tournament my father forces me to participate in using the plan I'll be using during my next heist. If I win, I use it, if I lose, I change it. Chess is a boring old board game which is the key to my fortune. I am the Black Falcon, this is my life on the board and against the law...
Not enough ratings
56 Chapters
Alpha's Check Mate
Alpha's Check Mate
A dangerous game, full of pitfalls. A dispute of power, money and desire. On one side of the board, the deputy Alpha Lauren Jauregui, and on the other, the wife of a magnate, Karla Camila Cabello. In this game, only one will fall. Who will have the best strategy? Who will better know how to play? Who will checkmate? Place your bets, the game will begin.
Not enough ratings
73 Chapters
HOW TO LOVE
HOW TO LOVE
Is it LOVE? Really? ~~~~~~~~~~~~~~~~~~~~~~~~ Two brothers separated by fate, and now fate brought them back together. What will happen to them? How do they unlock the questions behind their separation? ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
10
2 Chapters
How to Settle?
How to Settle?
"There Are THREE SIDES To Every Story. YOURS, HIS And The TRUTH."We both hold distaste for the other. We're both clouded by their own selfish nature. We're both playing the blame game. It won't end until someone admits defeat. Until someone decides to call it quits. But how would that ever happen? We're are just as stubborn as one another.Only one thing would change our resolution to one another. An Engagement. .......An excerpt -" To be honest I have no interest in you. ", he said coldly almost matching the demeanor I had for him, he still had a long way to go through before he could be on par with my hatred for him. He slid over to me a hot cup of coffee, it shook a little causing drops to land on the counter. I sighed, just the sight of it reminded me of the terrible banging in my head. Hangovers were the worst. We sat side by side in the kitchen, disinterest, and distaste for one another high. I could bet if it was a smell, it'd be pungent."I feel the same way. " I replied monotonously taking a sip of the hot liquid, feeling it burn my throat. I glanced his way, staring at his brown hair ruffled, at his dark captivating green eyes. I placed a hand on my lips remembering the intense scene that occurred last night. I swallowed hard. How? I thought. How could I be interested?I was in love with his brother.
10
16 Chapters
How To Survive Werewolves
How To Survive Werewolves
Emily wakes up one morning, trapped inside a Wattpad book she had read the previous night. She receives a message from the author informing her that it is her curse to relive everything in the story as one of the side characters because she criticized the book. Emily has to survive the story and put up with all the nonsense of the main character. The original book is a typical blueprint Wattpad werewolf story. Emily is thrown into this world as the main character's best friend, Catherine/Kate. There are many challenges and new changes to the story that makes thing significantly more difficult for Kate. Discover this world alongside Kate and see things from a different perspective. TW: Mentions of Abuse If you are a big fan of the typical "the unassuming girl is the mate of the alpha and so everything in the book resolves around that" book, this book is not for you. This is more centered around the best friend who is forgotten during the book because the main character forgets about her best friend due to her infatuation with the alpha boy.
10
116 Chapters

Related Questions

What Are The System Requirements For Conan Exiles On Windows?

6 Answers2025-10-19 04:33:38
To truly enjoy 'Conan Exiles' on Windows, you’ll want to make sure your system is up to the task. At the very least, you should be looking at a Windows 7 or later operating system. The ideal fit is a 64-bit version of Windows. I started there, but it quickly became clear that for a smooth experience, you'll definitely want an OS that can handle the intensity of the game! Now, let’s talk about the specifications that really make a difference. For the minimum requirements, a processor like Intel Core i3 or an AMD FX-4100 should suffice, alongside 6GB of RAM. Graphics-wise, you'll need something in the ballpark of Nvidia GeForce GTX 660 or AMD Radeon HD 7870. But if you’re like me, and you want everything running smoothly with great visuals, aiming higher is key! For optimal performance, a good upgrade would be an Intel Core i5 or an AMD Ryzen 5 paired with at least 8GB of RAM. Don’t forget about your graphics card – a GTX 970 or RX 580 will truly let you savor the game’s stunning world without those pesky lag moments. Also, keep in mind that having 40GB of free hard drive space is necessary to accommodate the game’s hefty data. Enjoying the vast lands of 'Conan Exiles' requires commitment, so gear up properly!

Who Is The Author Of Gathering Wives With A System Novels?

5 Answers2025-10-21 06:50:24
I got hooked on 'Gathering Wives with a System' because of its cheeky premise, and after digging through the translation notes and chapter credits I learned it's written by Fei Zhi. The name shows up across the official novel pages and most of the fan translation posts, so that's the authorial credit that keeps popping up. When I recommend it to friends I usually mention Fei Zhi first, because knowing the author helps when you want to find other works by the same person or check the release schedule. If you're browsing forums, you'll also see people comparing Fei Zhi's style to other system-based romcoms — same humor beats and world-building habits, but a distinct voice that leans into clever dialog and quirky side characters. I really enjoy how Fei Zhi balances the comedic system mechanics with surprisingly heartfelt moments — feels like a guilty pleasure with genuine warmth.

When Does The System Awakens: Rise Of The Champion Release?

5 Answers2025-10-21 17:25:29
I can't stop grinning — 'The System Awakens: Rise of the Champion' officially releases on November 14, 2025. The publisher announced a global digital launch at 00:00 UTC on that day, which means fans in different time zones will get access as their clocks hit the moment. Physical copies are hitting shelves the same week, with many bookstores and online retailers listing street date deliveries between November 14–17 depending on shipping and region. Preorders have already stacked up a neat array of bonuses: an exclusive short story, a glossy art card set for early buyers, and a limited-run hardback deluxe edition that includes author notes and a map. There's also an audiobook narrated by a couple of familiar voices from the scene, scheduled to drop in late November. I preordered the deluxe because I love those little extras — can’t resist the maps and marginalia — and I’m counting down the days with a ridiculous level of excitement.

What Is The Main Power System In 'Defense Kingdom'?

4 Answers2025-06-11 01:49:35
In 'Defense Kingdom', the power system revolves around 'Guardian Stones', mystical relics that bestow unique abilities upon their wielders. These stones are scattered across the kingdom, each tied to a specific element—earth, fire, water, or wind. Warriors who bond with a stone gain elemental mastery, like summoning earthquakes or controlling flames, but the real twist is their synergy. When multiple stones align, their combined energy creates devastating spells or impenetrable barriers. The system emphasizes teamwork, as solo users hit limits fast. What's fascinating is the stones' sentience. They choose their bearers based on personality, not strength. A timid healer might bond with a water stone, while a fiery rebel ignites a fire stone. The stones also evolve, unlocking new powers as their wielder grows emotionally. This isn't just magic; it's a relationship. The lore dives deep into how these bonds shape the kingdom's politics, with factions vying for control of rare stones. It's a fresh take on elemental magic, blending strategy, character growth, and epic battles.

Who Is The Main Villain In 'System Of Twin Daggers'?

5 Answers2025-06-11 10:54:22
In 'System of Twin Daggers', the main villain is a shadowy figure known as the Obsidian Monarch. This character isn't just a typical evil overlord—they represent the corruption of power and the decay of ancient traditions. The Monarch manipulates events from behind the scenes, using a network of spies and assassins to destabilize kingdoms. Their motives are complex, blending personal vendettas with a twisted vision of 'purifying' the world through chaos. What makes the Obsidian Monarch terrifying is their unpredictability. They don’t seek conquest but rather the collapse of order, making them a villain who thrives in ambiguity. Their mastery of illusion magic allows them to appear anywhere, whispering lies that turn allies into enemies. The protagonist often struggles to pinpoint their true location or intentions, adding layers of psychological tension to the story. The Monarch’s presence lingers even when they’re off-page, a constant threat woven into the narrative’s fabric.

Is 'System Of Twin Daggers' Being Adapted Into A TV Series?

5 Answers2025-06-11 23:20:19
Rumors about 'System of Twin Daggers' getting a TV adaptation have been swirling for months, but nothing’s confirmed yet. The web novel’s popularity makes it a prime candidate, though. Fans are speculating about which studio might pick it up—Netflix or HBO would be ideal given their track record with fantasy adaptations. Casting choices are already a hot topic; everyone’s debating who could pull off the dual protagonists’ chemistry. The story’s intricate politics and action-packed sequences would translate brilliantly to screen, but the magic system might need simplifying for viewers. The author’s cryptic tweets about 'exciting projects' fuel hope, but until there’s an official announcement, it’s all just wishful thinking. If it happens, expect explosive fan reactions—this series has a cult following.

What Is The Power System In 'Hegemony Of Mysteries'?

4 Answers2025-06-11 23:47:06
In 'Hegemony of Mysteries', the power system is a labyrinth of arcane hierarchies and eldritch secrets. At its core, practitioners channel 'Mystery Essence', a nebulous energy drawn from forgotten legends and unsolved enigmas. The more obscure the knowledge they wield, the deadlier their spells become. Scholars categorize abilities into 'Veils'—each representing a layer of understanding. Lower Veils manipulate basic phenomena like shadow or sound, while higher Veils rewrite local reality, bending time or spawning cursed artifacts. What fascinates me is the cost. Power demands sacrifice: memories, emotions, or even one's name can vanish with each spell. The protagonist juggles this brilliantly, trading fragments of his past to unlock apocalyptic techniques. The system mirrors the theme—truth is power, but ignorance might be survival. It’s not just magic; it’s a philosophical battleground wrapped in gothic horror.

Who Are The Main Villains In 'That Time I Reincarnated As A Siren With A System'?

4 Answers2025-06-11 16:06:45
The main antagonists in 'That Time I Reincarnated as a Siren with a System' are as layered as the ocean depths. The Abyssal Collective, a hive-minded legion of corrupted merfolk, serves as the primary threat. Their leader, Nerex the Hollow, is a former siren king whose soul was consumed by a parasitic void entity. He commands tides with a flick of his wrist and twists minds into loyal husks. The secondary villain is Lady Vespa, a human admiral who hunts sirens for their magic-infused scales. Her fleet deploys sonic disruptors that paralyze supernatural beings, and her obsession borders on genocidal. The System itself occasionally acts as an antagonist, imposing lethal quests that force the protagonist to choose between morality and survival. The villains aren’t just evil—they’re reflections of the story’s themes: exploitation, addiction to power, and the cost of defiance.
Explore and read good novels for free
Free access to a vast number of good novels on GoodNovel app. Download the books you like and read anywhere & anytime.
Read books for free on the app
SCAN CODE TO READ ON APP
DMCA.com Protection Status