Question

solve the following system of equations graphically on the set of axes below.
$y = \frac{3}{5}x - 1$
$y = -x + 7$
plot two lines by clicking the graph.
click a line to delete it.

Explanation:

Step1: Find intercepts for $y=\frac{3}{5}x-1$

• y-intercept (x=0): $y=\frac{3}{5}(0)-1=-1$, so point $(0, -1)$
• x-intercept (y=0): $0=\frac{3}{5}x-1 \implies \frac{3}{5}x=1 \implies x=\frac{5}{3}\approx1.67$, so point $(\frac{5}{3}, 0)$

Step2: Find intercepts for $y=-x+7$

• y-intercept (x=0): $y=-(0)+7=7$, so point $(0, 7)$
• x-intercept (y=0): $0=-x+7 \implies x=7$, so point $(7, 0)$

Step3: Find intersection algebraically

Set $\frac{3}{5}x-1=-x+7$
$\frac{3}{5}x+x=7+1$
$\frac{3}{5}x+\frac{5}{5}x=8$
$\frac{8}{5}x=8$
$x=8\times\frac{5}{8}=5$
Substitute $x=5$ into $y=-x+7$: $y=-5+7=2$
Intersection point is $(5, 2)$

Answer:

The solution to the system is the intersection point of the two lines: $(5, 2)$
To plot the lines:

1. For $y=\frac{3}{5}x-1$: plot $(0, -1)$ and $(\frac{5}{3}, 0)$, then draw the line through them.
2. For $y=-x+7$: plot $(0, 7)$ and $(7, 0)$, then draw the line through them.

The lines cross at $(5, 2)$.