Question

What is the point of intersection when the system of equations below is graphed on the coordinate plane?

y = 4 - x

2y = 8 - 2x

Answer 1

They are the same line

Answer 2

Infinite Solution

Explanation:

Given : System of equation

`y=4-x`

`2y=8-2x`

Point of intersection of the system of equation is solution of x and y.

using substitution method to solve for x and y

Put y=4-x into 2y=8-2x

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

`8-2x=8-2x`

LHS=RHL

Here, Left hand side expression is equal to right hand side expression.

Infinite number of solution.

If we graph both equation line would be coincide.

Please see the attachment for graph.

Hence, The point of intersection becomes a line. ( Infinite solution )