Question

How do you solve the system of equations `4x - 2y = - 30` and `- 2x - 10y = - 18`?

Answer 1

See the entire solution process below:

Explanation:

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

`-2x - 10y = -18`

`-2x - 10y + color(red)(10y) = -18 + color(red)(10y)`

`-2x - 0 = -18 + 10y`

`-2x = -18 + 10y`

`(-2x)/color(red)(-2) = (-18 + 10y)/color(red)(-2)`

`(color(red)(cancel(color(black)(-2)))x)/cancel(color(red)(-2)) = (-18)/color(red)(-2) + (10y)/color(red)(-2)`

`x = 9 - 5y`

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

`4(color(red)(9 - 5y)) - 2y = -30`

`(4 xx color(red)(9)) - (4 xx color(red)(5y)) - 2y = -30`

`36 - 20y - 2y = -30`

`36 - 22y = -30`

`36 - color(red)(36) - 22y = -30 - color(red)(36)`

`0 - 22y = -66`

`-22y = -66`

`(-22y)/color(red)(-22) = (-66)/color(red)(-22)`

`(color(red)(cancel(color(black)(-22)))y)/cancel(color(red)(-22)) = 3`

`y = 3`

Step 3) Substitute `color(red)(3)` for `y` in the solution to the second equation at the end of Step 1:

`x = 9 - (5 xx color(red)(3))`

`x = 9 - 15`

`x = -6`

The solution to this system of equations is:

`x = -6` and `y = 3`