SOLUTION: solve the system by substitution 6(x+2)-y=31 5x-2(y-3)=23

Question 23686: solve the system by substitution
6(x+2)-y=31
5x-2(y-3)=23
Answer by longjonsilver(2297) (Show Source): You can put this solution on YOUR website!
6(x+2)-y=31 --eqn1
5x-2(y-3)=23 --eqn2

eqn1 is re-arranged as follows:
6(x+2)-y=31
6(x+2)=31+y
6(x+2)-31=y

so, y = 6(x+2)-31. --eqn3

5x-2(y-3)=23
5x-2y+6 = 23
5x-2y = 17

Now sub eqn3 into our simplified version of eqn2 as follows:
5x-2y = 17 becomes
5x-2(6(x+2)-31) = 17
5x-2(6x+12)-31) = 17
5x-2(6x-19) = 17
5x-12x+38 = 17
-7x+38 = 17
-7x = -21
x = -21/-7
--> x = 3

So, now find y:
y = 6(x+2)-31
y = 6(3+2)-31
y = 6(5)-31
y = 30-31
--> y = -1

Now, check in the other equation that your solution works there too:
5x-2(y-3)=23
5(3)-2(-1-3)=23
15-2(-1-3)=23
15-2(-4)=23
15+8=23
23=23 --> correct

Now you KNOW that your answers are correct.

jon.

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