Questions: Solve the system of equations. y=8x y=3x+30

Solve the system of equations. y=8x y=3x+30
Transcript text: Solve the system of equations. \[ \begin{array}{l} y=8 x \\ y=3 x+30 \end{array} \]
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Solution

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Solution Steps

To solve the system of equations, we can set the two equations equal to each other since they both equal \( y \). This will allow us to solve for \( x \). Once we have \( x \), we can substitute it back into either equation to find \( y \).

Step 1: Set the Equations Equal

We have the system of equations: \[ y = 8x \] \[ y = 3x + 30 \] To find the values of \( x \) and \( y \), we set the two equations equal to each other: \[ 8x = 3x + 30 \]

Step 2: Solve for \( x \)

Rearranging the equation gives: \[ 8x - 3x = 30 \] \[ 5x = 30 \] Dividing both sides by 5, we find: \[ x = 6 \]

Step 3: Substitute \( x \) to Find \( y \)

Now, we substitute \( x = 6 \) back into one of the original equations to find \( y \). Using the first equation: \[ y = 8(6) = 48 \]

Final Answer

The solution to the system of equations is: \[ \boxed{x = 6} \] \[ \boxed{y = 48} \]

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