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 [tex]y=mx+b[/tex]:
[tex]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[/tex]
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: https://brainly.com/question/10022596
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