Question

solving a system of linear equations by graphing
solve this system of linear equations:
$4x - 2y = 8$ $y = \frac{3}{2}x - 2$
step 1: plot the x - intercept of the first equation.
step 2: plot the y - intercept of the first equation
step 3: plot the y - intercept of the second equation.
the correct points are shown.

Explanation:

Step1: Find x-intercept of $4x-2y=8$

Set $y=0$:
$4x - 2(0) = 8$
$4x = 8$
$x = 2$
So x-intercept is $(2, 0)$

Step2: Find y-intercept of $4x-2y=8$

Set $x=0$:
$4(0) - 2y = 8$
$-2y = 8$
$y = -4$
So y-intercept is $(0, -4)$

Step3: Find y-intercept of $y=\frac{3}{2}x-2$

For slope-intercept form $y=mx+b$, $b$ is y-intercept. Here $b=-2$, so y-intercept is $(0, -2)$

Step4: Identify intersection point

The two lines intersect at $(2, 0)$, which is the solution.

Answer:

The solution to the system is $\boldsymbol{(2, 0)}$
The completed table for the first equation $4x-2y=8$ is:

$x$	$y$
2	0