Question

Solve each system by elimination

8x-y=-26
10x+7y=-16

Answer 1

Answer: x = -3 and y = 2.

Step-by-step explanation: To solve the system of equations by elimination, we want to eliminate one of the variables by adding or subtracting the equations. One way to do this is to multiply one of the equations by a constant so that when we add or subtract the equations, one of the variables is eliminated.

In this case, we can eliminate the variable y by multiplying the first equation by 7 and the second equation by 1, so that the y terms have opposite coefficients:

56x - 7y = -182

10x + 7y = -16

Now, we can add the two equations to eliminate y:

66x = -198

Dividing both sides by 66, we get:

x = -3

Now that we have the value of x, we can substitute it into one of the original equations to find the value of y. Let's use the first equation:

8x - y = -26

8(-3) - y = -26

-24 - y = -26

Adding 24 to both sides, we get:

-y = -2

Dividing both sides by -1, we get:

y = 2

Therefore, the solution to the system of equations is x = -3 and y = 2.

Answer 2

x = -3

y = 2

Explanation:

8x - y = -26

10x + 7y = -16

Times the first equation by 7

56x - 7y = -182

10x + 7y = -16

66x = -198

x = - 3

Now put -3 in for x and solve for y

8(-3) - y = -26

-24 - y = -26

-y = -2

y = 2

Let's check

8(-3) - 2 = -26

-24 - 2 = -26

-26 = -26

So, x = -3 and y = 2 is the correct answer.