Solving systems by substitution method

Question

solve the system by using substitution method.
2(x+2y)=12
-6x=5y-8

Answer 1

2(x + 2y) = 12           divide both sides by 2

x + 2y = 6                  subtract 2y from both sides

x = -2y + 6

 

-6x = 5y - 8               substitute for x from above

-6(-2y + 6) = 5y - 8   distribute

12y - 36 = 5y - 8       subtract 5y from both sides

7y - 36 = -8               add 36 to both side

7y = 28                     divide both sides by 7

y = 4

 

x = -2(4) + 6

x = -8 + 6

x = -2

 

{(-2, 4)}

Answer 2

2(x+2y)=12

-6x=5y-8

using the first equation...

2(x+2y)=12

(x+2y)=6

x=6-2y

substitute

-6(6-2y)=5y-8

-36+12y=5y-8

12y-5y=36-8

7y=28

y=4

using the second equation...

-6x=5(4)-8

-6x=20-8

-6x=12

x=-2

(-2,4)  is the solution