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Does the system of equations have no solution, one solution, or infinitely many solutions? \( \begin{array}{l}2 x+y=2 \\ y=-2 x-1\end{array} \) The system has Choose...

Ask by Ramirez Pearson. in the United States
Jan 22,2025

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The system has **no solution**.

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Beyond the Answer

To determine the nature of the solutions for the given system of equations, we can graph the lines represented by each equation. The first equation, \(2x + y = 2\), can be rearranged to \(y = -2x + 2\), which has a slope of -2. The second equation, \(y = -2x - 1\), also has a slope of -2 but intersects the y-axis at -1. Since these two lines have the same slope but different y-intercepts, they are parallel and will never intersect—meaning this system has no solution. If you're ever confused about the relationship between two linear equations, just graph them! If they cross at a point, you've got one solution. If they're the same line, congrats—infinitely many solutions! But if they’re parallel, like here, then you can confidently say there's no solution!

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