Question

How do you solve `6x+9y=3` and `x+4y=-2`?

Answer 1

See a solution process below:

Explanation:

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

`x + 4y = -2`

`x + 4y - color(red)(4y) = -2 - color(red)(4y)`

`x + 0 = -2 - 4y`

`x = -2 - 4y`

Step 2) Substitute `(-2 - 4y)` for `x` in the first equation and solve for `y`:

`6x + 9y = 3` becomes:

`6(-2 - 4y) + 9y = 3`

`(6 xx -2) - (6 xx 4y) + 9y = 3`

`-12 - 24y + 9y = 3`

`-12 + (-24 + 9)y = 3`

`-12 + (-15)y = 3`

`-12 - 15y = 3`

`-12 + color(red)(12) - 15y = 3 + color(red)(12)`

`0 - 15y = 15`

`-15y = 15`

`(-15y)/color(red)(-15) = 15/color(red)(-15)`

`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 = -2 - 4y` becomes:

`x = -2 - (4 xx -1)`

`x = -2 - (-4)`

`x = -2 + 4`

`x = 2`

The Solution Is:

`x = 2` and `y = -1`

Or

`(2, -1)`