Question

solve the following system of equations graphically on the set of axes below.
$y = -2x - 1$
$y = \frac{1}{3}x + 6$
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: text box submit answer

Explanation:

Step1: Find intersection algebraically

Set $-2x - 1 = \frac{1}{3}x + 6$
Multiply all terms by 3: $-6x - 3 = x + 18$
Rearrange: $-6x - x = 18 + 3$
$-7x = 21$
$x = -3$
Substitute $x=-3$ into $y=-2x-1$: $y=-2(-3)-1=6-1=5$

Step2: Graph first line ($y=-2x-1$)

Identify intercepts:
y-intercept: when $x=0$, $y=-1$ → point $(0, -1)$
x-intercept: when $y=0$, $0=-2x-1$ → $x=-\frac{1}{2}$ → point $(-0.5, 0)$
Plot these two points and draw the line.

Step3: Graph second line ($y=\frac{1}{3}x+6$)

Identify intercepts:
y-intercept: when $x=0$, $y=6$ → point $(0, 6)$
x-intercept: when $y=0$, $0=\frac{1}{3}x+6$ → $x=-18$ (outside the given axes, so use another point: when $x=3$, $y=\frac{1}{3}(3)+6=7$ → point $(3,7)$)
Plot $(0,6)$ and $(3,7)$ and draw the line.

Step4: Verify intersection

The two lines intersect at $(-3, 5)$, which matches the algebraic solution.

Answer:

The solution to the system is $(-3, 5)$