Question

How do you solve the following system of equations?: `2x + 15y = -4 , -x + 3y=12`?

Answer 1

See the entire solution process below:

Explanation:

Step 1) Solve the second equation for `x`:

`-x + 3y = 12`

`-x + 3y - color(red)(3y) = 12 - color(red)(3y)`

`-x + 0 = 12 - 3y`

`-x = 12 - 3y`

`-1 xx -x = -1(12 - 3y)`

`x = (-1 xx 12) - (-1 xx 3y)`

`x = -12 + 3y`

Step 2) Substitute `-12 + 3y` for `x` in the first equation and solve for `y`:

`2x + 15y = -4` becomes:

`2(-12 + 3y) + 15y = -4`

`(2 xx -12) + (2 xx 3y) + 15y = -4`

`-24 + 6y + 15y = -4`

`-24 + 21y = -4`

`color(red)(24) - 24 + 21y = color(red)(24) - 4`

`0 + 21y = 20`

`21y = 20`

`(21y)/color(red)(21) = 20/color(red)(21)`

`(color(red)(cancel(color(black)(21)))y)/cancel(color(red)(21)) = 20/21`

`y = 20/21`

Step 3) Substitute `20/21` for `y` in the solution to the second equation at the end of Step 1 and calculate `x`:

`x = -12 + 3y` becomes:

`x = -12 + (3 xx 20/21)`

`x = -12 + 20/7`

`x = (7/7 xx -12) + 20/7`

`x = -84/7 + 20/7`

`x = -64/7`

The solution is: `x = -64/7` and `y = 20/21` or `(-64/7, 20/21)`