Question

solve the following system of equations graphically on the set of axes below.
$y = \frac{1}{2}x + 4$
$y = -x + 7$
plot two lines by clicking the graph.
click a line to delete it.

Explanation:

Step1: Find two points for \( y = \frac{1}{2}x + 4 \)

When \( x = 0 \), \( y=\frac{1}{2}(0)+4 = 4 \), so one point is \( (0, 4) \).
When \( x = 2 \), \( y=\frac{1}{2}(2)+4 = 1 + 4 = 5 \), so another point is \( (2, 5) \).

Step2: Find two points for \( y = -x + 7 \)

When \( x = 0 \), \( y=-0 + 7 = 7 \), so one point is \( (0, 7) \).
When \( x = 1 \), \( y=-1 + 7 = 6 \), so another point is \( (1, 6) \).

Step3: Graph the lines and find intersection

Plot the lines using the points. The intersection of \( y = \frac{1}{2}x + 4 \) and \( y = -x + 7 \) is found by solving \( \frac{1}{2}x + 4=-x + 7 \).
Add \( x \) to both sides: \( \frac{3}{2}x + 4 = 7 \).
Subtract 4: \( \frac{3}{2}x = 3 \).
Multiply by \( \frac{2}{3} \): \( x = 2 \).
Substitute \( x = 2 \) into \( y=-x + 7 \): \( y=-2 + 7 = 5 \). So the intersection is \( (2, 5) \).

Answer:

The solution to the system is \( (2, 5) \) (the point where the two lines intersect when graphed).