Question

How do you solve the system of linear equations `2x − 3y = 3` and `5x − 4y = 4`?

Answer 1

There are two methods. 1. solve for one variable and then substitute.
2. Add or subtract the equations so that one variable is eliminated then substitute.

Explanation:

`2x -3y = 3` add 3y to both sides

`2x -3y + 3y = -3y +3` gives

`2x = +3y +3` divide both sides by 2

`(2x)/2 = (+3y)/2 + 3/2` which gives.

`x = +3/2 y + 3/2` Now substitute into the other equation

`5x -4y = 4 = 5(+3/2y + 3/2) -4y = 4` which gives

`(+15/2)y + 15/2 -4y = 4` multiply everything by 2

`2(+15/2)y + 2 (15/2) -4y = 4`

`+15y -4y + 15 = 4` subtract 15 from both sides

`11y + 15 -15 = 4 -15`

`11y = - 11` divide both sides by 11

`(11y/11 = -11/11` gives

`y = -1`

`2x -3(-1) = 3`

`2x + 3 = 3` subtract 3 from both sides

`2x + 3 -3 = 3 -3` so

`2x = 0` divide both sides by two

`2x/2 = 0/2`

`x = 0`