Questions: COURSE OUTLINE Complete this assessment to review what you've learned. It will not count rowara your grade. Use the table to answer the question. course toots x-value y-value if y=x+6 y-value if y=2x+3 0 6 3 1 7 5 2 8 7 3 9 9 4 10 11 A system of equations is displayed in the table. What is the solution for the system? (1 point)

COURSE OUTLINE Complete this assessment to review what you've learned. It will not count rowara your grade. Use the table to answer the question. course toots x-value y-value if y=x+6 y-value if y=2x+3 0 6 3 1 7 5 2 8 7 3 9 9 4 10 11 A system of equations is displayed in the table. What is the solution for the system? (1 point)
Transcript text: COURSE OUTLINE Complete this assessment to review what you've learned. It will not count rowara your grade. Use the table to answer the question. course toots \begin{tabular}{|l|l|l|} \hline$x$-value & $y$-value if $y=x+6$ & $y$-value if $y=2 x+3$ \\ \hline 0 & 6 & 3 \\ \hline 1 & 7 & 5 \\ \hline 2 & 8 & 7 \\ \hline 3 & 9 & 9 \\ \hline 4 & 10 & 11 \\ \hline \end{tabular} A system of equations is displayed in the table. What is the solution for the system? (1 point) $\square$ $\square$ Check answer Remaining Attempts : 3
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Solution

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Solution Steps

To solve the system of equations given in the table, we need to find the point where the two equations \( y = x + 6 \) and \( y = 2x + 3 \) intersect. This means finding the values of \( x \) and \( y \) that satisfy both equations simultaneously. We can do this by setting the two equations equal to each other and solving for \( x \), then substituting back to find \( y \).

Step 1: Set the Equations Equal to Each Other

To find the intersection of the two equations \( y = x + 6 \) and \( y = 2x + 3 \), we set them equal to each other: \[ x + 6 = 2x + 3 \]

Step 2: Solve for \( x \)

Rearrange the equation to solve for \( x \): \[ x + 6 = 2x + 3 \implies 6 - 3 = 2x - x \implies 3 = x \]

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

Substitute \( x = 3 \) back into one of the original equations to find \( y \). Using \( y = x + 6 \): \[ y = 3 + 6 = 9 \]

Final Answer

\(\boxed{(x, y) = (3, 9)}\)

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