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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