Solve using Substitution

Question

Solve using Substitution: 3x+4y=15

                                      x-y=5

Answer 1

3x+4y=15

x-y=5

 

Solve for x in the 2nc equation:   x-y=5 

add y to both sides...  x=y+5

 

Plug that back into equation 1:

 

3(y+5) + 4y = 15

3y+15 + 4y = 15

 

7y +15 = 15

subtract 15 from both sides

7y +15-15 = 15-15

7y = 0

y=0

 

Plug that back into equation 1 or 2... For ease let's use equation 2:  x-y=5

 

x-0=5

x=5

 

Check our answers:  3x+4y=15  ...  3(5) + 4(0) = 15 ...   15 = 15   this checks

                               x-y=5  ...  5-0 = 5  ...  5=5   this also checks

 

So x=5 and y=0

Answer 2

3x + 4y = 15
x - y = 5

 

Solve one of the equations for one of the variables. I recommend the second equation because it is simpler.

x = 5 - y

 

Plug it in for the variable in the other equation.

3(5 - y) + 4y = 15

15 - 3y + 4y = 15

y = 0

 

Plug in y then solve for x.

x = 5 - y

x = 5 - 0

x = 5