Pregunta
Solve the system by substitution. \[ \begin{aligned} y & =6 x-2 \\ y & =5 x\end{aligned} \]
Ask by Vargas Williams. in the United States
Feb 03,2025
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Respuesta verificada por el tutor
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The solution is \( x=2 \) and \( y=10 \).
Solución
Solve the system of equations \( y=6x-2;y=5x \).
Solve the system of equations by following steps:
- step0: Solve using the substitution method:
\(\left\{ \begin{array}{l}y=6x-2\\y=5x\end{array}\right.\)
- step1: Substitute the value of \(y:\)
\(6x-2=5x\)
- step2: Move the variable to the left side:
\(6x-2-5x=0\)
- step3: Subtract the terms:
\(x-2=0\)
- step4: Move the constant to the right side:
\(x=0+2\)
- step5: Remove 0:
\(x=2\)
- step6: Substitute the value of \(x:\)
\(y=6\times 2-2\)
- step7: Simplify:
\(y=10\)
- step8: Calculate:
\(\left\{ \begin{array}{l}x=2\\y=10\end{array}\right.\)
- step9: Check the solution:
\(\left\{ \begin{array}{l}x=2\\y=10\end{array}\right.\)
- step10: Rewrite:
\(\left(x,y\right) = \left(2,10\right)\)
The solution to the system of equations by substitution is \( (x,y) = (2,10) \).
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Simplifique esta solución The Deep Dive
To solve the system by substitution, we can set the right-hand sides of the equations equal to each other since both equal \( y \): \[ 6x - 2 = 5x \] Now, subtract \( 5x \) from both sides: \[ 6x - 5x - 2 = 0 \] This simplifies to: \[ x - 2 = 0 \] Now, solve for \( x \): \[ x = 2 \] Next, substitute \( x = 2 \) back into either of the original equations to find \( y \). Using \( y = 5x \): \[ y = 5(2) \] \[ y = 10 \] So the solution to the system is: \[ (x, y) = (2, 10) \]
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