Question

How do you solve the following system?: `5x +y =2, 13x -5y = -2`

Answer 1

See the entire solution process below:

Explanation:

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

`5x + y = 2`

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

`0 + y = -5x + 2`

`y = -5x + 2`

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

`13x - 5y = -2` becomes:

`13x - 5(-5x + 2) = -2`

`13x - (5 xx -5x) - (5 xx 2) = -2`

`13x + 25x - 10 = -2`

`38x - 10 = -2`

`38x - 10 + color(red)(10) = -2 + color(red)(10)`

`38x - 0 = 8`

`38x = 8`

`(38x)/color(red)(38) = 8/color(red)(38)`

`(color(red)(cancel(color(black)(38)))x)/cancel(color(red)(38)) = (2 xx 4)/color(red)(2 xx 19)`

`x = (color(red)(cancel(color(black)(2))) xx 4)/color(red)(cancel(2) xx 19)`

`x = 4/19`

Step 3) Substitute `4/19` for `x` in the solution to the first equation at the end of Step 1 and calculate `y`:

`y = -5x + 2` becomes:

`y = (-5 xx 4/19) + 2`

`y = -20/19 + 2`

`y = -20/19 + (19/19 xx 2)`

`y = -20/19 + 38/19`

`y = 18/19`

The solution is: `x = 4/19` and `y = 18/19` or `(4/19, 18/19)`