Question

How do you solve the following linear system: `x+8y=3, 4x+5y=-2`?

Answer 1

See the solution process below:

Explanation:

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

`x + 8y = 3`

`x + 8y - color(red)(8y) = 3 - color(red)(8y)`

`x + 0 = 3 - 8y`

`x = 3 - 8y`

Step 2) Subsitute `3 - 8y` for `x` in the second equation and solve for `y`:

`4x + 5y = -2` becomes:

`4(3 - 8y) + 5y = -2`

`(4 * 3) - (4 * 8y) + 5y = -2`

`12 - 32y + 5y = -2`

`12 + (-32 + 5)y = -2`

`12 - 27y = -2`

`-color(red)(12) + 12 - 27y = -color(red)(12) - 2`

`0 - 27y = -14`

`-27y = -14`

`(-27y)/color(red)(-27) = (-14)/color(red)(-27)`

`(color(red)(cancel(color(black)(-27)))y)/cancel(color(red)(-27)) = 14/27`

`y = 14/27`

Step 3) Substitute `14/27` for `y` in the solution to the first equation at the end of Step 1 and calculate `x`:

`x = 3 - 8y` becomes:

`x = 3 - (8 * 14/27)`

`x = 3 - 112/27`

`x = (3 * 27/27) - 112/27`

`x = 81/27 - 112/27`

`x = -31/27`

The solution is: `x = -31/27` and `y = 14/27` or `(-31/27, 14/27)`