Question

solve the following system of equations graphically on the set of axes below.
$y = \frac{1}{5}x + 1$
$y = -x + 7$
plot two lines by clicking the graph.
click a line to delete it.

Explanation:

Step1: Graph \( y = \frac{1}{5}x + 1 \)

To graph this line, we can find two points. When \( x = 0 \), \( y = \frac{1}{5}(0)+1 = 1 \), so the y - intercept is \( (0,1) \). When \( x = 5 \), \( y=\frac{1}{5}(5)+1=1 + 1=2 \), so we have another point \( (5,2) \). Plot these two points and draw a line through them.

Step2: Graph \( y=-x + 7 \)

For this line, when \( x = 0 \), \( y=-0 + 7=7 \), so the y - intercept is \( (0,7) \). When \( x = 7 \), \( y=-7 + 7 = 0 \), so we have the point \( (7,0) \). Plot these two points and draw a line through them.

Step3: Find the intersection point

The solution to the system of equations is the point where the two lines intersect. By looking at the graph (or by solving the equations algebraically: set \( \frac{1}{5}x+1=-x + 7 \), \( \frac{1}{5}x+x=7 - 1 \), \( \frac{1 + 5}{5}x=6 \), \( \frac{6}{5}x=6 \), \( x = 5 \), then \( y=-5 + 7=2 \)), the intersection point is \( (5,2) \).

Answer:

The solution to the system of equations is \( x = 5,y = 2 \) (or the point \( (5,2) \))