Question

solve the following system of equations graphically on the set of axes below.
$y = \frac{1}{6}x + 7$
$y = -2x - 6$
plot two lines by clicking the graph.
click a line to delete it.

Explanation:

Step1: Find intersection by equating equations

Set \(\frac{1}{6}x + 7=-2x - 6\) to find \(x\) value of intersection.

Step2: Solve for \(x\)

Multiply all terms by 6 to eliminate fraction: \(x + 42=-12x - 36\).
Add \(12x\) to both sides: \(13x + 42=-36\).
Subtract 42: \(13x=-78\).
Divide by 13: \(x = -6\).

Step3: Find \(y\) using \(x=-6\)

Substitute \(x = -6\) into \(y=-2x - 6\): \(y=-2(-6)-6=12 - 6 = 6\).

Answer:

The solution is \(x=-6\), \(y = 6\) (the point \((-6,6)\) is the intersection of the two lines).