Question

How do you solve the system of equations `7x + 3y = - 9` and `3y = x + 15`?

Answer 1

See a solution process below:

Explanation:

Step 1) Solve each equation for `3y`:

• Equation 1:

`7x + 3y = -9`

`7x - color(red)(7x) + 3y = -9 - color(red)(7x)`

`0 + 3y = -9 - 7x`

`3y = -9 - 7x`

• Equation 2: is already solved for `3y`

`3y = x + 15`

Step 2) Because the left side of both equations are equal we can equate the right sides of the equations and solve for `x`:

`-9 - 7x = x + 15`

`-9 - color(blue)(15) - 7x + color(red)(7x) = x + color(red)(7x) + 15 - color(blue)(15)`

`-24 - 0 = 1x + color(red)(7x) + 0`

`-24 = (1 + color(red)(7))x`

`-24 = 8x`

`(-24)/color(red)(8) = (8x)/color(red)(8)`

`-3 = (color(red)(cancel(color(black)(8)))x)/cancel(color(red)(8))`

`-3 = x`

`x = -3`

Step 3) Substitute `-3` for `x` in either of the equations from Step 1 and solve for `y`:

`3y = x + 15` becomes:

`3y = -3 + 15`

`3y = 12`

`(3y)/color(red)(3) = 12/color(red)(3)`

`(color(red)(cancel(color(black)(3)))y)/cancel(color(red)(3)) = 4`

`y = 4`

The Solution Is:

`x = -3` and `y = 4`

Or

`(-3, 4)`