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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.

1 answer

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.