Answer:
(3,2)
Step-by-step explanation:
We are given the system:
3x-y=7
2x-2y=2.
We are asked to solve this by substitution. We need to pick an equation and pick a variable from that equation to solve for that variable.
I really like either for this. Some people might go with the first one though. Let's do that. I will solve the first one for y.
3x-y=7
Subtract 3x on both sides:
-y=-3x+7
Divide both sides by -1:
y=3x-7
Now we are ready for substitution. We are going to plug this equation into the second equation giving us:
2x-2y=2 with y=3x-7 gives us:
2x-2(3x-7)=2
Distribute:
2x-6x+14=2
Combine like terms:
-4x+14=2
Subtract 14 on both sides:
-4x =2-14
Simplify:
-4x =-12
Divide both sides by -4:
x =-12/-4
Simplify:
x =3
So using y=3x-7 and x=3, I will find y now.
y=3x-7 if x=3
y=3(3)-7 (I inserted 3 for x since we had x=3)
y=9-7 (Simplified)
y=2 (Simplified)
The answer is (x,y)=(3,2).
