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I AM STUCK AND NEED HELP will give 30 points

A system of equations is graphed on the coordinate plane.

2y=3x−1
4y=6x−2
Select the number of solutions for the system of equations from the drop-down menu.

infinite solutions
one solution
or
no solutions

I AM STUCK AND NEED HELP will give 30 points A system of equations is graphed on the-example-1

1 Answer

3 votes

Answer: A) infinite solutions

Step-by-step explanation:

Despite there only being one line shown, there are actually two lines here. One just happens to be directly on top of the other.

We can see this by noting that 2y = 3x-1 turns into 4y = 6x-2 when we multiply both sides by 2. Multiplying both sides by the same number keeps the same equation, so that's why we have identical graphs.

The two identical graphs intersect each other infinitely many times, leading to infinitely many solutions. All solutions are (x,y) points on the blue line. Two such solutions are (1,1) and (3,4). All solutions are of the form
\left(x, (3x-1)/(2)\right)

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