Question

llowing system of equations graphically on the set of axe
$y = -x + 5$
$2x - y = 7$
plot two lines by clicking the graph.
click a line to delete it.

Explanation:

Step1: Rewrite 2nd equation to slope-intercept

$2x - y = 7 \implies y = 2x - 7$

Step2: Find intercepts for $y=-x+5$

• y-intercept: set $x=0$, $y=5$ → $(0,5)$
• x-intercept: set $y=0$, $0=-x+5 \implies x=5$ → $(5,0)$

Step3: Find intercepts for $y=2x-7$

• y-intercept: set $x=0$, $y=-7$ → $(0,-7)$
• x-intercept: set $y=0$, $0=2x-7 \implies x=\frac{7}{2}=3.5$ → $(3.5,0)$

Step4: Solve for intersection algebraically

Set $-x+5=2x-7$
$5+7=2x+x$
$12=3x \implies x=4$
Substitute $x=4$ into $y=-x+5$: $y=-4+5=1$
Intersection point: $(4,1)$

Answer:

The solution to the system is $(4, 1)$, and the lines are plotted as follows:

1. Line $y=-x+5$: passes through $(0,5)$ and $(5,0)$
2. Line $y=2x-7$: passes through $(0,-7)$ and $(3.5,0)$