Question

Solve systems of equations
y=-2x+6 y=1/2x-9

Answer 1

To solve the system of equations, you need to set the two equations equal to each other and solve for x. Once you have the value of x, substitute it back into one of the original equations to solve for y. The solution to the system of equations is x = 30 and y = -54.

Step-by-step explanation:

To solve the system of equations:

y = -2x + 6

y = 1/2x - 9

1. Set the two equations equal to each other:

-2x + 6 = 1/2x - 9

1. Add 2x to both sides to isolate the x term:

6 + 2x = 1/2x - 9 + 2x

1. Add 9 to both sides to isolate the constant term:

15 + 2x = 1/2x + 2x

1. Combine like terms:

15 + 2x = 5/2x

1. Multiply both sides by 2 to eliminate the fraction:

30 + 4x = 5x

1. Subtract 4x from both sides to isolate the x term:

30 + 4x - 4x = 5x - 4x

1. Simplify:

30 = x

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

y = -2(30) + 6

1. Perform the calculations:

y = -60 + 6

1. Simplify:

y = -54

Therefore, the solution to the system of equations is x = 30 and y = -54.