Question

Solve this system by elimination. SHOW ALL OF YOUR WORK.
5x-4y=3
-10x+7y=-4​

Answer 1

Explanation:

Look at the coefficients of x: One is a multiple of the other. This makes it easy to eliminate the x terms.

Multiply the first equation by 2:

10x - 8y = 6

Then add it to the second equation:

 10x - 8y = 6

-10x + 7y = -4

--------------------

 0x - y = 2, therefore, y = -2.

Now substitute -2 for y in either of the equations and solve for x:

5x - 4(-2) = 3

5x = -5

x = -1

(x,y) = (-1,-2)

Answer 2

Hi! Your answer is x = -1, y = -2. We can write in coordinate form as (-1,-2)

Please see an explanation for a better and clear understanding to your problem.

Any questions about my answer and explanation can be asked through comments! :)

Explanation:

`\large{\begin{cases} 5x-4y=3 \\ -10x+7y=-4 \end{cases}}`

By elimination method, we can eliminate either x-term or y-term. It depends on your choice or desire. Notice that both equations cannot be eliminated because if we add x-term up, we would get -5x which doesn't even eliminate x-term. Same goes to y-term. Now the question will pop up in your head - Then how do we eliminate either x-term or y-term?

Simple, multiply the whole equation to make one of the terms have same absolute value. Notice if we multiply the whole first equation by 2, we would get x-term from 5x to 10x. Then we add 10x and -10x up, we would get 0 and finally get x-term to be eliminated.

Therefore, multiply the whole first equation by 2.

`\large{5x-4y=3}\\\large{5x(2)-4y(2)=3(2)}\\\large{10x-8y=6}`

Next, rewrite the equation.

`\large{\begin{cases} 10x-8y=6 \\ -10x+7y=-4 \end{cases}}`

Then we are able to eliminate x-term by adding up between first and second equation.

`\large{(10x-10x)+(-8y+7y)=6-4}\\\large{0-y=2}\\\large{-y=2}\\\large{y=-2}`

We've finally got the y-value. But we are not done yet. What we are going to do next is to find x-value.

Simply substituting y = -2 in any given equations. You can either substitute y = -2 in one equation only if you are pretty certain enough or two equations if you think that you value safety/quality more than time. I'll be substituting y = -2 in two equations to demonstrate how substituting the solution in two equations get you to the same answer.

Substituting in First Equation

`\large{5x-4y=3}`

Substitute y = -2 in the equation. It's the best to use an original equation instead of rewritten equation.

`\large{5x-4(-2)=3}\\\large{5x+8=3}\\\large{5x=3-8}\\\large{5x=-5}\\\large{x=-1}`

Substituting in Second Equation

`\large{-10x+7y}=-4`

Substitute y = -2 in the equation.

`\large{-10x+7(-2)=-4}\\\large{-10x-14=-4}\\\large{-14+4=10x}\\\large{-10=10x}\\\large{-1=x}`

Notice how substituting in two equations give the exact same answer in the end. We've finally got the solution.

We can conclude that when x = -1, y =-2.