Question

How do you solve the system of equations `x- 2y = 5` and `- 3x + 4y = - 11`?

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`:

`-3x + 4y = -11` becomes:

`-3(5 + 2y) + 4y = -11`

`(-3 * 5) + (-3 * 2y) + 4y = -11`

`-15 - 6y + 4y = -11`

`-15 + (-6 + 4)y = -11`

`-15 - 2y = -11`

`color(red)(15) - 15 - 2y = color(red)(15) - 11`

`0 - 2y = 4`

`-2y = 4`

`(-2y)/color(red)(-2) = 4/color(red)(-2)`

`(color(red)(cancel(color(black)(-2)))y)/cancel(color(red)(-2)) = -2`

`y = -2`

Step 3) Substitute `-2` for `y` in the solution the the first equation at the end of Step 1 and calculate `x`:

`x = 5 + 2y` becomes:

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

`x = 5 - 4`

`x = 1`

The solution is `x = 1` and `y = -2` or `(1, -2)`