Vaughn Pope
06/04/2023 · Middle School

Graph the system below and write its solution. \[ \begin{array}{c}y=2 x+1 \\ -4 x+2 y=2\end{array} \] Note that you can also answer "No solution" or "Infinitely many" solu

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Solve the system of equations \( 2x+1=y;-4x+2y=2 \). Solve the system of equations by following steps: - step0: Solve using the substitution method: \(\left\{ \begin{array}{l}2x+1=y\\-4x+2y=2\end{array}\right.\) - step1: Rewrite the expression: \(\left\{ \begin{array}{l}y=2x+1\\-4x+2y=2\end{array}\right.\) - step2: Substitute the value of \(y:\) \(-4x+2\left(2x+1\right)=2\) - step3: Simplify: \(2=2\) - step4: Calculate: \(\left(x,y\right) = \left(x,2x+1\right),x \in \mathbb{R}\) - step5: Alternative Form: \(\textrm{Infinitely many solutions}\) The system of equations has infinitely many solutions. This means that the lines represented by the equations intersect at every point on the line \(y = 2x + 1\), and there is no specific point of intersection.

Quick Answer

The system has infinitely many solutions.
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