Question

How do you solve the system of equations `6x - 24y = 30` and `8x + 6y = 40`?

Answer 1

See a solution process below:

Explanation:

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

`6x - 24y = 30`

`(6x - 24y)/color(red)(6) = 30/color(red)(6)`

`(6x)/color(red)(6) - (24y)/color(red)(6) = 5`

`(color(red)(cancel(color(black)(6)))x)/cancel(color(red)(6)) - (color(red)(cancel(color(black)(24)))4y)/cancel(color(red)(6)) = 5`

`x - 4y = 5`

`x - 4y + color(red)(4y) = 5 + color(red)(4y)`

`x - 0 = 5 + 4y`

`x = 5 + 4y`

Step 2) Substitute `(5 + 4y)` for `x` in the second equation and solve for `y`:

`8x + 6y = 40` becomes:

`8(5 + 4y) + 6y = 40`

`(8 * 5) + (8 * 4y) + 6y = 40`

`40 + 32y + 6y = 40`

`40 + (32 + 6)y = 40`

`40 + 38y = 40`

`-color(red)(40) + 40 + 38y = -color(red)(40) + 40`

`0 + 38y = 0`

`38y = 0`

`(38y)/color(red)(38) = 0/color(red)(38)`

`(color(red)(cancel(color(black)(38)))y)/cancel(color(red)(38)) = 0`

`y = 0`

Step 3) Substitute `0` for `y` in the solution to the first equation at the end of Step 1 and calculate `x`:

`x = 5 + 4y` becomes:

`x = 5 + (4 * 0)`

`x = 5 + 0`

`x = 5`

The solution is: `x = 5` and `y = 0` or `(5, 0)`