Question

the following system of equations graphically on the set of axes below
$y = -x + 7$
$y = \frac{3}{2}x - 8$
plot two lines by clicking the graph.
click a line to delete it.
(graph with x-axis from -10 to 10 and y-axis from -10 to 10)
answer attempt 1 out of 2
solution: blank box submit answer

Explanation:

Step1: Set the two equations equal

Since \(y=-x + 7\) and \(y=\frac{3}{2}x-8\), we set \(-x + 7=\frac{3}{2}x-8\).

Step2: Solve for \(x\)

Add \(x\) to both sides: \(7=\frac{3}{2}x+x - 8\). Combine like - terms: \(7=\frac{3x+2x}{2}-8\), so \(7=\frac{5x}{2}-8\). Add 8 to both sides: \(7 + 8=\frac{5x}{2}\), \(15=\frac{5x}{2}\). Multiply both sides by \(\frac{2}{5}\): \(x=15\times\frac{2}{5}=6\).

Step3: Solve for \(y\)

Substitute \(x = 6\) into \(y=-x + 7\). Then \(y=-6 + 7=1\).

Answer:

\((6,1)\)