Question

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

Explanation:

Step1: Find intersection by solving equations

Set $-\frac{1}{6}x + 7 = 2x - 6$.
Multiply both sides by 6: $-x + 42 = 12x - 36$.

Step2: Solve for x

Add x to both sides: $42 = 13x - 36$.
Add 36 to both sides: $78 = 13x$.
Divide by 13: $x = 6$.

Step3: Find y

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

Answer:

The solution is $(6, 6)$ (the point where the two lines intersect when graphed).