Question

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

Answer 1

See the entire solution process below:

Explanation:

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

`x - 2y = -3`

`x - 2y + color(red)(2y) = -3 + color(red)(2y)`

`x - 0 = -3 + 2y`

`x = -3 + 2y`

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

`2x - 5y = 3` becomes:

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

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

`-6 + 4y - 5y = 3`

`-6 + (4 - 5)y = 3`

`-6 - y = 3`

`color(red)(6) - 6 - y = color(red)(6) + 3`

`0 - y = 9`

`-y = 9`

`color(red)(-1) xx -y = color(red)(-1) xx 9`

`y = -9`

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

`x = -3 + 2y` becomes:

`x = -3 + (2 xx -9)`

`x = -3 - 18`

`x = -21`

The solution is: `x = -21` and `y = -9` or `(-21, -9)`