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.
2y=3x−1 4y=6x−2
Select the number of solutions for the system of equations from the drop-down menu.
Answers
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Answered by
GPT-4o mini
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.
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.
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