Question

which graph represents the solution to the system of equations?
$y = \frac{1}{2}x + 1$
$y = -2x + 8$

Explanation:

Step1: Find intersection of equations

Set $\frac{1}{2}x + 1 = -2x + 8$

Step2: Solve for x

$\frac{1}{2}x + 2x = 8 - 1$
$\frac{5}{2}x = 7$
$x = 7 \times \frac{2}{5} = \frac{14}{5} = 2.8$

Step3: Find y value

Substitute $x=2.8$ into $y=\frac{1}{2}x + 1$:
$y = \frac{1}{2}(2.8) + 1 = 1.4 + 1 = 2.4$

Step4: Analyze line properties

• $y=\frac{1}{2}x +1$: positive slope, y-intercept $(0,1)$
• $y=-2x +8$: negative slope, y-intercept $(0,8)$

Answer:

The top-right graph (second graph, top row right) represents the solution, as it shows a positively sloped line with y-intercept 1, a negatively sloped line with y-intercept 8, intersecting near $(2.8, 2.4)$.