Question

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.

Answer 1

To determine the number of solutions for the system of equations given by:

1. \(2y = 3x - 1\)
2. \(4y = 6x - 2\)

We can start by simplifying each equation.

For the first equation:
\[
2y = 3x - 1 \implies y = \frac{3}{2}x - \frac{1}{2}
\]

For the second equation:
\[
4y = 6x - 2 \implies y = \frac{3}{2}x - \frac{1}{2}
\]

Both equations simplify to the same line equation:
\[
y = \frac{3}{2}x - \frac{1}{2}
\]

Since both equations represent the same line, the system of equations has infinitely many solutions because every point on this line is a solution.

Therefore, the number of solutions for the system of equations is infinite.