Question

1. $y=3x-4$

$y=-\frac{1}{2}x+3$

Explanation:

Step1: Set equations equal to each other

$3x - 4 = -\frac{1}{2}x + 3$

Step2: Multiply by 2 to eliminate fraction

$6x - 8 = -x + 6$

Step3: Combine like terms for x

$6x + x = 6 + 8$
$7x = 14$

Step4: Solve for x

$x = \frac{14}{7} = 2$

Step5: Substitute x=2 into first equation

$y = 3(2) - 4 = 6 - 4 = 2$

Step6: Verify with second equation

$y = -\frac{1}{2}(2) + 3 = -1 + 3 = 2$

Answer:

The solution to the system is $(2, 2)$. To graph:

1. For $y=3x-4$: plot the y-intercept $(0, -4)$, then use slope 3 to plot $(1, -1)$, draw the line.
2. For $y=-\frac{1}{2}x+3$: plot the y-intercept $(0, 3)$, then use slope $-\frac{1}{2}$ to plot $(2, 2)$, draw the line.

The lines intersect at $(2, 2)$.