Solve the following system of equations graphically on the set of axes below.

Plot two lines by clicking the graph.
Click a line to delete it.

Ask by Cruz Clarke. in the United States

Mar 30,2025

Question

Solve the following system of equations graphically on the set of axes below. $$ y=\frac{3}{2} x-4 $$ $$ y=-\frac{1}{3} x+7 $$ Plot two lines by clicking the graph. Click a line to delete it. $$ y $$

UpStudy AI · Accepted Answer

We have the following system of equations to solve graphically:
1. $$ y = \frac{3}{2} x - 4 $$
2. $$ y = -\frac{1}{3} x + 7 $$
To plot the lines, we can find two points for each equation.

For the first equation $$ y = \frac{3}{2} x - 4 $$:
- When $$ x = 0 $$: 
  $$ y = \frac{3}{2}(0) - 4 = -4 $$ 
  (Point: (0, -4))
- When $$ x = 4 $$: 
  $$ y = \frac{3}{2}(4) - 4 = 2 $$ 
  (Point: (4, 2))

For the second equation $$ y = -\frac{1}{3} x + 7 $$:
- When $$ x = 0 $$: 
  $$ y = -\frac{1}{3}(0) + 7 = 7 $$ 
  (Point: (0, 7))
- When $$ x = 6 $$: 
  $$ y = -\frac{1}{3}(6) + 7 = 5 $$ 
  (Point: (6, 5))
Now, plot the points on the graph:
- For the first line, plot points (0, -4) and (4, 2).
- For the second line, plot points (0, 7) and (6, 5).

Draw the lines through these points to visualize the intersection.
To find the intersection point graphically, look for the point where the two lines cross on the graph. This point represents the solution to the system of equations.
The intersection point of the two lines is the solution to the system of equations. You can find this point by observing the graph where the two lines intersect.

Solve the following system of equations graphically on the set of axes below.

Plot two lines by clicking the graph.
Click a line to delete it.

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Solve the following system of equations graphically on the set of axes below. Plot two lines by clicking the graph. Click a line to delete it.