Question

Directions: Graph each system of equations. Then determine whether the system has no solution, one solution, or infinitely many solutions. If the system has one solution, name it—-NEED the intersection point (x,y).

Answer 1

One solution: (-3, -1)

Step-by-step explanation:

First, we need to graph the lines, so we need to identify two points on each line. So, we need to give values to the variable x and calculate the value of y.

For y = (4/3)x + 3, we get:

If x = 3, then:

y = (4/3)(3) + 3 = 4 + 3 = 7

If x = 0, then:

y = (4/3)(0) + 3 = 0 + 3 = 3

For y = (-2/3)x - 3, we get:

If x = 3, then:

y = (-2/3)(3) - 3 = -2 - 3 = -5

If x = 0, then:

y = (-2/3)(0) - 3 = 0 - 3 = -3

So, we have the points (3, 7) and (0, 3) for the first equation and the points (3, -5) and (0, -3) for the second equation. Therefore, the graph of the lines is:

Therefore, the system has one solution and the solution of the system is the intersection point (-3, -1).