Question

Use the elimination method to solve this system.

Answer 1

Answer:

The solution for this system is: $x = -1, y = 1$

Step-by-step explanation:

The problem states that we have to solve this system by the elimination method

In the elimination method, we transform the system in such a way that one variable can cancel each other. With this, we find the result of the other variable. Then, we can replace the variable we found in any of the equations, and we have the value of the variable that we had initially canceled.

In this problem, we have the following system:

$1) -6x + 5y = 1$

$2) 6x + 4y = -10$

If we add equations 1) and 2), the variable x is going to be eliminated

$1) + 2)$

$-6x + 6x + 5y + 4y = 1 - 10$

$9y = -9$

$y = \frac{-9}{9}$

$y = -1$

Now, we can replace the value of y in any of the equations, to find x:

I will replace in equation 2)

$6x + 4y = -10$

$6x + 4(-1) = -10$

$6x = -6$

$x = \frac{-6}{6}$

$x = -1$

The solution for this system is: $x = -1, y = 1$