Question

How do you solve the following system: `6x+2y=-4, x-5y=-9`?

Answer 1

See a solution process below:

Explanation:

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

`x - 5y = -9`

`x - 5y + color(red)(5y) = -9 + color(red)(5y)`

`x - 0 = -9 + 5y`

`x = -9 + 5y`

Step 2) Substitute `(-9 + 5y)` for `x` in the first equation and solve for `y`:

`6x + 2y = -4` becomes:

`6(-9 + 5y) + 2y = -4`

`(6 xx -9) + (6 xx 5y) + 2y = -4`

`-54 + 30y + 2y = -4`

`-54 + (30 + 2)y = -4`

`-54 + 32y = -4`

`-54 + color(red)(54) + 32y = -4 + color(red)(54)`

`0 + 32y = 50`

`32y = 50`

`(32y)/color(red)(32) = 50/color(red)(32)`

`(color(red)(cancel(color(black)(32)))y)/cancel(color(red)(32)) = 25/16`

`y = 25/16`

Step 3) Substitute `25/16` for `y` in the solution to the second equation at the end of Step 1 and calculate `x`:

`x = -9 + 5y` becomes:

`x = -9 + (5 xx 25/16)`

`x = (16/16 xx -9) + 125/16`

`x = -144/16 + 125/16`

`x = -19/16`

The Solution Is:

`x = -19/16` and `y = 25/16`

Or

`(-19/16, 25/16)`