Question

How do you solve the system of equations `x + 2y = - 2` and `3x + 4y = 6`?

Answer 1

The solution is `(10,-6)`.

Explanation:

Solve the system:

`"Equation 1":` `x+2y=-2`

`"Equation 2":` `3x+4y=6`

The equations are in standard form for a linear equation. The solution, `(x,y)`, is the point that they have in common. I am going to solve the system by substitution.

Solve Equation 1 for `x`.

`x=-2y-2`

Substitute `-2y-2` for `x` in Equation 2 and solve for `y`.

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

`-6y-6+4y=6`

Simplify.

`-2y-6=6`

Add `6` to both sides.

`-2y=6+6`

Simplify.

`-2y=12`

Divide both sides by `-2`.

`y=12/(-2)`

Simplify.

`y=-6`

Substitute `-6` for `y` in Equation 1 and solve for `x`.

`x+2(-6)=-2`

`x-12=-2`

Add `12` to both sides.

`x=-2+12`

`x=10`

The solution is `(10,-6)`.

graph{(x+2y+2)(3x+4y-6)=0 [-16.02, 16.02, -8.01, 8.01]}