Question

Solve by substitution. Show each step of your work. 5x + y = 15 3x + 2y = 16

Answer 1

Given equations are 5x + y = 15 and 3x + 2y = 16.

Solving first equation in the form y=mx+b,

5x + y = 15

y = -5x + 15

Substituting y= -5x+15 from first equation into second equation :-

3x + 2y = 16

3x + 2·(-5x + 15) = 16

3x - 10x + 30 = 16

-7x + 30 = 16

7x = 30 - 16 = 14

x = 2

Substituting x=2 into first equation :-

5x + y = 15

5(2) + y = 15

10 + y = 15

y = 15 - 10

y = 5

So final answers are x=2, y=5.

Answer 2

5x + y = 15 => y = 15 - 5x

3x + 2y = 16

3x + 2.(15 - 5x) = 16

3x + 30 - 10x = 16

-7x + 30 = 16

-7x = 16 - 30

-7x = -14

x = -14/-7

x = 2

5x + y = 15

5.2 + y = 15

10 + y = 15

y = 15 - 10

y = 5