Solve by substitution method 15x-20y7 5y-3 10x?

Answer 1

15x - 20y = 7

5y - 3 = 10x

Let's solve the second equation for y.

5y - 3 = 10x add 3 to both sides;

5y = 10x + 3 divide by 5 to both sides;

y = 2x + 3/5

Substitute the expression 2x + 3/5 for y to the first equation.

15x - 20y = 7

15x - 20(2x + 3/5) = 7 multiply by 20 each term of the parentheses;

15x -40x - 60/5 = 7

- 25x - 12 = 7 add 12 to both sides;

-25x = 19 multiply by -1 to both sides;

25x = -19 divide by 25 to both sides;

x = -19/25

Substitute -19/25 for x to y = 2x + 3/5

y = 2x + 3/5

y = 2(-19/25) + 3/5

y = -38/25 + 3/5 multiply 3/5 by 5/5;

y = -38/25 + 15/25

y =-23/25

The solution set is (-19/25, -23/25)

Check:

1. 15 x - 20y = 7

15(-19/25) - 20(-23/25) = 7?

-285/25 + 460/25 = 7 ?

175/25 = 7 ?

7 = 7

2. 5y - 3 = 10x

5(-23/25) - 3 = 10(-19/25) ?

-115/25 - 3 = -190/25 ?

-115/25 - 3(25/25) = -190/25 ?

-115/25 - 75/25 = -190/25 ?

-190/25 = -190 / 25 or,

-38/5 = -38/5

The solution set is (1/5, 1)