Question

How do you solve the system of equations `2x + 2y = 8` and `1x + 1y = 4`?

Answer 1

`y=4-x`

Refer to the explanation.

Explanation:

Solve the system of equations:

`"Equation 1":` `2x+2y=8`

`"Equation 2":` `x+y=4` (No coefficient is understood to be `1`.)

These are linear equations in standard form: `Ax+By=C`. They are solved simultaneously by substitution. The values for `x` and `y` represent the point of intersection between the lines on a graph.

I will start with `"Equation 2"` because it is simplest.

`y=4-x`

Substitute `4-x` for `y` in `"Equation 1"` and solve for `x`.

`2x+2(4-x)=8`

`2x+8-2x=8`

Subtract `8` from both sides.

`2x-2x=8-8`

`0=0`

There is an infinite number of solutions.

The only valid solution is the equation `y=4-x`. So there will be no point of intersection.

graph{y=4-x [-10, 10, -5, 5]}