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.
answer
attempt 1 out of 2
solution:

Explanation:

Step1: Find intercepts for $y=-\frac{1}{6}x+7$

• y-intercept: Set $x=0$, $y=7$ → point $(0,7)$
• x-intercept: Set $y=0$, $0=-\frac{1}{6}x+7$ → $\frac{1}{6}x=7$ → $x=42$ (use $x=6$, $y=-\frac{1}{6}(6)+7=6$ → point $(6,6)$ for graphing)

Step2: Find intercepts for $y=2x-6$

• y-intercept: Set $x=0$, $y=-6$ → point $(0,-6)$
• x-intercept: Set $y=0$, $0=2x-6$ → $2x=6$ → $x=3$ → point $(3,0)$

Step3: Find intersection algebraically

Set $-\frac{1}{6}x+7=2x-6$
Multiply all terms by 6: $-x+42=12x-36$
Rearrange: $42+36=12x+x$ → $78=13x$ → $x=6$
Substitute $x=6$ into $y=2x-6$: $y=2(6)-6=6$
Intersection point: $(6,6)$

Answer:

The solution to the system is $\boldsymbol{(6, 6)}$ (this is the point where the two lines intersect on the graph)