Bird Mccarthy
05/30/2024 · Senior High School
5. \( 6 x-2 y=-4 \) \( y=3 x+2 \)
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Step-by-step Solution
Solve the system of equations \( 6x-2y=-4;y=3x+2 \).
Solve the system of equations by following steps:
- step0: Solve using the substitution method:
\(\left\{ \begin{array}{l}6x-2y=-4\\y=3x+2\end{array}\right.\)
- step1: Substitute the value of \(y:\)
\(6x-2\left(3x+2\right)=-4\)
- step2: Simplify:
\(-4=-4\)
- step3: Calculate:
\(\left(x,y\right) = \left(x,3x+2\right),x \in \mathbb{R}\)
- step4: Alternative Form:
\(\textrm{Infinitely many solutions}\)
The system of equations \(6x-2y=-4\) and \(y=3x+2\) has infinitely many solutions.
Quick Answer
The system has infinitely many solutions.
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