Question

solve the following system of equations graphically on the set of axes below.
$y = -\frac{1}{3}x - 1$
$y = x + 7$
plot two lines by clicking the graph.
click a line to delete it.

Explanation:

Step1: Graph \( y = -\frac{1}{3}x - 1 \)

To graph this line, we can find two points. When \( x = 0 \), \( y = -1 \). When \( x = 3 \), \( y = -\frac{1}{3}(3) - 1 = -2 \). So we have points \((0, -1)\) and \((3, -2)\). Plot these points and draw the line.

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

For this line, when \( x = 0 \), \( y = 7 \). When \( x = -7 \), \( y = 0 \). So points are \((0, 7)\) and \((-7, 0)\). Plot these and draw the line.

Step3: Find Intersection

The solution to the system is the point where the two lines intersect. By graphing (or solving algebraically: set \( -\frac{1}{3}x - 1 = x + 7 \), \( -\frac{1}{3}x - x = 7 + 1 \), \( -\frac{4}{3}x = 8 \), \( x = -6 \), then \( y = -6 + 7 = 1 \)), the intersection is at \((-6, 1)\).

Answer:

The solution is \( x = -6 \), \( y = 1 \) (or the point \((-6, 1)\)).