Question

How do you solve the system of equations `-3x + 7y = 8` and `x + 2y = - 7`?

Answer 1

See a solution process below:

Explanation:

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

`x + 2y = -7`

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

`x + 0 = -7 - 2y`

x = -7 - 2y#

Step 2) Substitute `(-7 - 2y)` for `x` in the first equation and solve for `y`:

`-3x + 7y = 8` becomes:

`-3(-7 - 2y) + 7y = 8`

`(-3 xx -7) + (-3 xx -2y) + 7y = 8`

`21 + 6y + 7y = 8`

`21 + (6 + 7)y = 8`

`21 + 13y = 8`

`21 - color(red)(21) + 13y = 8 - color(red)(21)`

`0 + 13y = -13`

`13y = -13`

`(13y)/color(red)(13) = -13/color(red)(13)`

`(color(red)(cancel(color(black)(13)))y)/cancel(color(red)(13)) = -1`

`y = -1`

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

x = -7 - 2y# becomes:

x = -7 - (2 xx -1)#

x = -7 - (-2)#

x = -7 + 2#

`x = -5`

**The Solution Is:``x = -5`and`y = -1`or`(-5, -1)#