Question

How do you solve the following system?: `x +2y =5, -4x +y = -3`

Answer 1

See a solution process below:

Explanation:

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

`x + 2y = 5`

`x + 2y - color(red)(2y) = 5 - color(red)(2y)`

`x + 0 = 5 - 2y`

`x = 5 - 2y`

Step 2) Substitute `(5 - 2y)` for `x` in the second equation and solve for `y`:

`-4x + y = -3` becomes:

`-4(5 - 2y) + y = -3`

`(-4 xx 5) - (-4 xx 2y) + y = -3`

`-20 - (-8y) + y = -3`

`-20 + 8y + y = -3`

`-20 + 8y + 1y = -3`

`-20 + (8 + 1)y = -3`

`-20 + 9y = -3`

`-20 + color(red)(20) + 9y = -3 + color(red)(20)`

`0 + 9y = 17`

`9y = 17`

`(9y)/color(red)(9) = 17/color(red)(9)`

`(color(red)(cancel(color(black)(9)))y)/cancel(color(red)(9)) = 17/9`

`y = 17/9`

Step 3) Substitute `17/9` for `y` in the solution to the first equation at the end of Step 1 and calculate `x`:

`x = 5 - 2y` becomes:

`x = 5 - (2 xx 17/9)`

`x = 5 - 34/9`

`x = (9/9 xx 5) - 34/9`

`x = 45/9 - 34/9`

`x = (45 - 34)/9`

`x = 11/9`

The Solution Is:

`x = 11/9` and `y = 17/9`

Or

`(11/9, 17/9)`