How many solutions does the system have?

Mathematics

1 answer:

umka21 [38]4 years ago

3 0

One solution

<h2>Explanation:</h2>

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

<h3>Case 1. No solution.</h3>

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

<h3>Case 2. One solution.</h3>

This happens when the lines intersect at a single point.

<h3>Case 1. Infinitely many solutions</h3>

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.

<h2>Learn more:</h2>

Parametric equations: brainly.com/question/10022596

#LearnWithBrainly

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