Question

Solution:17.Graph each system and determine the number of solutions that it has. If it has one solution,name it.B. 2x-y=1y=-3

Answer 1

Part A)

First, draw the graph of each of the given equations:

The graph of x+2y=4 is shown as a solid, orange line.

The graph of y=(-1/2)x+2 is shown as a dotted, blue line.

Notice that both graphs overlap.

A solution to the system of equations is a point shared by the graph of both lines. In this case, since both lines overlap, every point on the lines is a solution to the system of equations.

Therefore, the system has infinitely many solutions.

Part B)

The graph of 2x-y=1 is shown in green, and the graph of y=-3 is shown in purple:

As we can see, both lines intersect at (-1,-3).

Therefore, this system has one solution. The solution is (-1,-3).