The solution to the system of equations is (2.8, -6.8).
To solve the system of equations using elimination:
Multiply the top equation by 2 and the bottom equation by 1:
-2x-12y=76
-2x+2y=-8
Add the top and bottom equations together:
-10y=68
Divide both sides by -10 to solve for y:
y=-6.8
Substitute -6.8 for y in either of the original equations to solve for x:
-x-6(-6.8)=38
-x+40.8=38
-x=-2.8
x=2.8
Therefore, the solution to the system of equations is (2.8, -6.8).
Detailed steps:
Step 1: Multiply the top equation by 2 and the bottom equation by 1:
(-x-6y)*2 = (38)*2
-2x-12y = 76
-2x+2y = -8
Step 2: Add the top and bottom equations together:
-2x-12y + -2x+2y = 76 - 8
-4x-10y = 68
Step 3: Divide both sides by -10 to solve for y:
(-4x-10y)/-10 = 68/-10
y = 6.8
Step 4: Substitute -6.8 for y in either of the original equations to solve for x:
-x-6(-6.8) = 38
-x+40.8 = 38
-x = -2.8
x = 2.8
Therefore, the solution to the system of equations is (2.8, -6.8).