Question

Number graph ranging from negative two to ten on the x and y axes. A line labeled y equals begin fraction three over two end fraction times x is drawn on the graph. A second line, labeled y equals begin fraction negative one over two end fraction x plus four, is drawn on the graph. What is the solution to the system of equations represented by these two lines? Responses (2, 0) (2, 0) (0, 4) (0, 4) (4, 2) (4, 2) (2, 3)

Answer 1

Explanation:

To find the solution to the system of equations represented by the two lines, we need to find the point where they intersect on the graph.

First, let's find the coordinates of the intersection point by solving the system of equations. We have:

y = (3/2)x (Equation 1)

y = (-1/2)x + 4 (Equation 2)

To find the intersection point, we need to set the two equations equal to each other:

(3/2)x = (-1/2)x + 4

Simplifying this equation, we get:

2x = 8

x = 4

Now that we know x = 4, we can substitute this value into either Equation 1 or Equation 2 to find the corresponding value of y:

y = (3/2)x

y = (3/2)(4)

y = 6

Therefore, the solution to the system of equations represented by the two lines is (4, 6).