Question

How do you solve this system of equations: `8x - y = - 5; 10x - y = - 7` ?

Answer 1

See the entire solution process below:

Explanation:

Step 1) Solve the first equation for `y` while keeping the equation balanced:

`8x - y = -5`

`8x - y - color(red)(8x) = -5 - color(red)(8x)`

`8x - color(red)(8x) - y = -5 - color(red)(8x)`

`-y = -5 - 8x`

`color(red)(-1) xx -y = color(red)(-1) xx(-5 - 8x)`

`y = 5 + 8x`

Step 2) Substitute `5 + 8x` for `y` in the second equation and solve for `x` while keeping the equation balanced:

`10x - (5 + 8x) = -7`

`10x - 5 - 8x = -7`

`10x - 8x - 5 = -7`

`2x - 5 = -7`

`2x - 5 + color(red)(5) = -7 + color(red)(5)`

`2x - 0 = -2`

`2x = -2`

`(2x)/color(red)(2) = -2/color(red)(2)`

`(color(red)(cancel(color(black)(2)))x)/cancel(color(red)(2)) = -1`

`x = -1`

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

`y = 5 + (8 xx -1)`

`y = 5 - 8`

`y = -3`

The solution is:

`x = -1` and `y = -3`