Question

How do you solve the system of equations `2x + 3y = 18` and `3x - 5= y`?

Answer 1

See a solution process below:

Explanation:

Step 1) Because the second equation is already solved for `y`, we can substitute `(3x - 5)` for `y` in the first equation and solve for `x`:

`2x + 3y = 18` becomes:

`2x + 3(3x - 5) = 18`

`2x + (3 xx 3x) - (3 xx 5) = 18`

`2x + 9x - 15 = 18`

`(2 + 9)x - 15 = 18`

`11x - 15 = 18`

`11x - 15 + color(red)(15) = 18 + color(red)(15)`

`11x - 0 = 33`

`11x = 33`

`(11x)/color(re)(11) = 33/color(re)(11)`

`(color(red)(cancel(color(black)(11)))x)/cancel(color(re)(11)) = 3`

`x = 3`

Step 2) Substitute `3` for `x` in the second equation and solve for `y`:

`3x - 5 = y` becomes:

`(3 xx 3) - 5 = y`

`9 - 5 = y`

`4 = y`

`y = 4`

The Solution Is: `x = 3` and `y = 4` or `(3, 4)`