2x – 2y = -4 and x + y = 8

Question

System of equations:

2x – 2y = -4 and x + y = 8

Solve for x and y

Answer 1

1. 2x−2y=−4
2. x+y=8

We can use the substitution or elimination method. I'll demonstrate the elimination method here:

Step 1: Multiply the second equation by 2 to make the coefficients of y in both equations the same:

1. 2x−2y=−4
2. 2(x+y)=2(8)

This becomes:

1. 2x−2y=−4
2. 2x+2y=16

Step 2: Add the two equations to eliminate y:(2x−2y)+(2x+2y)=−4+16

Combine like terms:

4x=12

Step 3: Solve for x:

x=412​=3

Step 4: Substitute the value of x back into one of the original equations. I'll use the second equation:

3+y=8

Step 5: Solve for y:

y=8−3=5

So, the solution to the system of equations isx=3 andy=5.

Answer 2

Step #1 : Take the simpler equation and solve for X.

x + y = 8

-y -y

x = 8 - y

Step #2: Substitute the new X value into the remaining equation.

(This should give you the numeric value of y)

2(8-y) -2y = -4

16 -2y -2y = -4

16 -4y = -4

-16 -16

-4y = -20

-4 -4

y=5

Step #3: Plug the numeric value of Y into the simple equation to solve for X.

(This should give you the numeric value of X)

x + y = 8

x + 5 = 8

-5 -5

x = 3

Step #4: CHECK your answer by substituting the x and y value into the remaining equation

2x - 2y = -4

2(3) -2(5) = -4

6 - 10 = -4

-4 = -4