Question

A system of equations is shown: 2x = -y 6 -4x 3y = 8. What is the solution to this system of equations?

1) (-1, -4)
2) (1, 4)
3) (4, 1)
4) (-4, -1)

Answer 1

The solution to the given system of equations is (x, y) = (13, -20).

Step-by-step explanation:

The given system of equations is:

2x = -y + 6

-4x + 3y = 8

To solve this system of equations, we can use the method of substitution or elimination. Let's use the elimination method.

Multiply the first equation by 3 and the second equation by 2 to eliminate the y variable:

6x = -3y + 18

-8x + 6y = 16

Add the two equations:

(6x + -8x) + (-3y + 6y) = 18 + 16

-2x + 3y = 34

Simplify the equation:

-2x + 3y = 34

We now have a new system of equations:

-2x + 3y = 34

-4x + 3y = 8

Subtract the second equation from the first equation:

(-2x + 3y) - (-4x + 3y) = 34 - 8

2x = 26

Divide both sides by 2:

x = 13

Substitute the value of x into one of the original equations to solve for y:

2(13) = -y + 6

26 = -y + 6

Subtract 6 from both sides:

20 = -y

Divide both sides by -1:

y = -20

Therefore, the solution to the system of equations is (x, y) = (13, -20).