Solve the system of equations by using either the substitution or the elimination method: 2(x+2)-2(y-6)=22

Question

4(x-6)+6(y-6)=_38

Answer 1

To solve the system of equations, we will use the substitution method.

First, let's solve the first equation for x:

2(x+2)-2(y-6)=22
2x + 4 - 2y + 12 = 22
2x - 2y + 16 = 22
2x - 2y = 6
x - y = 3 (dividing both sides by 2)

Now, we can substitute this expression for x in the second equation:

4(x-6)+6(y-6)= 38
4(x-6) + 6(y-6) = 38
4(x-6) + 6(x+2-6) = 38 (substituting x - y = 3)
4x - 24 + 6(x-4) = 38
4x - 24 + 6x - 24 = 38
10x - 48 = 38
10x = 86
x = 8.6

To find y, we substitute this value of x back into the first equation:

x - y = 3
8.6 - y = 3
-y = 3 - 8.6
-y = -5.6
y = 5.6

Therefore, the solution to the system of equations is x = 8.6 and y = 5.6.