Question

solve this system of equations by graphing. first graph the equations, and then type the solution.

$x - 2y = -8$

$y = \frac{5}{2}x$

click to select points on the graph.

Explanation:

Step1: Rewrite first equation to slope-intercept form

Solve $x-2y=-8$ for $y$:
$x-2y=-8$
$-2y = -x -8$
$y = \frac{1}{2}x + 4$

Step2: Identify key points for first line

For $y=\frac{1}{2}x + 4$:

• y-intercept: when $x=0$, $y=4$ → $(0,4)$
• x-intercept: when $y=0$, $0=\frac{1}{2}x +4$ → $x=-8$ → $(-8,0)$

Step3: Identify key points for second line

For $y=\frac{5}{2}x$:

• Origin point: when $x=0$, $y=0$ → $(0,0)$
• Second point: when $x=2$, $y=5$ → $(2,5)$

Step4: Find intersection of the two lines

Set $\frac{1}{2}x + 4 = \frac{5}{2}x$
$4 = \frac{5}{2}x - \frac{1}{2}x$
$4 = 2x$
$x=4$
Substitute $x=4$ into $y=\frac{5}{2}x$: $y=\frac{5}{2}(4)=10$
Intersection point: $(4,10)$

Answer:

$(4, 10)$