Question

How many solutions does the system have?

Answer 1

One solution

Explanation:

For a system of linear equations in two variables, we could have three possible cases:

Case 1. No solution.

This happens when the lines are parallel and have different y-intercepts.

Case 2. One solution.

This happens when the lines intersect at a single point.

Case 1. Infinitely many solutions

This happens when the lines are basically the same having the same slope and y-intercept.

So, let's rewrite our lines in Slope-intercept form $y=mx+b$:

$Line \ 1: \\ \\ 4x-2y = 8 \\ \\ 2y=4x-8 \\ \\ y=\frac{4}{2}x-\frac{8}{2} \\ \\ y=2x-4 \\ \\ \\ Line \ 2: \\ \\ 2x + y = 2 \\ \\ y=-2x+2$

As you can see, they have different slopes and y-intercepts. So they will intersect at a single point which is the solution of the system. By using graphing tool we get that this point is (1.5, -1) as indicated in the figure below.

Learn more:

Parametric equations: brainly.com/question/10022596

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