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Graph the system below and write its solution. \[ \begin{array}{l}y=-\frac{1}{2} x+3 \\ -x-2 y=-2\end{array} \]

Ask by Phillips Bolton. in the United States
Mar 14,2025

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There is no solution to the system of equations because the two lines are parallel and do not intersect.

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To graph the system of equations, we'll start by rewriting the second equation in slope-intercept form (y = mx + b). The second equation is: \[ -x - 2y = -2 \] Adding \( x \) to both sides gives us: \[ -2y = x - 2 \] Now, dividing every term by -2: \[ y = -\frac{1}{2}x + 1 \] Now we have two linear equations: 1. \( y = -\frac{1}{2}x + 3 \) 2. \( y = -\frac{1}{2}x + 1 \) Both lines have the same slope (-1/2). However, the second equation is a constant distance lower on the y-axis, indicating that they are parallel lines and will never intersect. Therefore, this system of equations has no solution. In graph form, both lines will be straight and parallel, indicating that they do not meet at any point on the graph.

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