Question

How do you solve the system of equations `4x + 2y = 16` and `3x + 3y = 18`?

Answer 1

Refer to the explanation for the process.

Explanation:

Solve system of equations:

We have two linear equations in standard form. We will use substitution to solve for `x` and `y`. The point `(x,y)` will be the point of intersection between the two lines.

Equation 1: `4x+2y=16`

Equation 2: `3x+3y=18`

Solve Equation 2 for `y`.

`3(x+y)=18`

Divide both sides by `3`.

`x+y=18/3`

Simplify.

`x+y=6`

Solve for `y`.

`y=6-x`

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

`4x+2(6-x)=16`

Expand.

`4x+12-2x=16`

Subtract `12` from both sides.

`4x-2x=16-12`

Simplify.

`2x=4`

Divide both sides by `2`.

`x=2`

Substitute `2` for `x` in Equation 1 and solve for `y`.

`3(2)+3y=18`

Simplify.

`6+3y=18`

Subtract `6` from both sides.

`3y=18-6`

Simplify.

`3y=12`

Divide both sides by `3`.

`y=12/3`

Simplify.

`y=4`

The point of intersection between the two lines is `(2,4)`.