Question

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

Explanation:

Step1: Graph \( y = -3x - 7 \)

Find two points on the line. When \( x = 0 \), \( y = -3(0) - 7 = -7 \), so the y - intercept is \( (0, -7) \). When \( y = 0 \), \( 0=-3x - 7\Rightarrow3x=-7\Rightarrow x = -\frac{7}{3}\approx - 2.33 \), so another point is \( (-\frac{7}{3},0) \). Plot these two points and draw the line.

Step2: Graph \( y = x - 3 \)

Find two points on the line. When \( x = 0 \), \( y = 0 - 3=-3 \), so the y - intercept is \( (0, - 3) \). When \( y = 0 \), \( 0=x - 3\Rightarrow x = 3 \), so another point is \( (3,0) \). Plot these two points and draw the line.

Step3: Find the intersection

The solution of the system of equations is the point where the two lines intersect. By solving the two equations simultaneously (or by looking at the graph), we set \( -3x - 7=x - 3 \).
\( -3x-x=-3 + 7\)
\( -4x = 4\)
\( x=-1 \)
Substitute \( x = - 1 \) into \( y=x - 3 \), we get \( y=-1-3=-4 \). So the intersection point is \( (-1,-4) \).

Answer:

The solution of the system of equations is \( x=-1,y = - 4 \) (or the point \( (-1,-4) \) is the solution).