Solve the following system of linear equations by first graphing the system. y=4x−5 y=−x+5

Answer 1

To graph the system of equations, we will plot both equations on the same graph:

Equation 1: y = 4x -5
Equation 2: y = -x + 5

Now plot the two equations:

For Equation 1, when x = 0:
y = 4(0) - 5
y = -5
Point: (0, -5)

When x = 1:
y = 4(1) - 5
y = -1
Point: (1, -1)

For Equation 2, when x = 0:
y = -(0) + 5
y = 5
Point: (0, 5)

When x = 1:
y = -(1) + 5
y = 4
Point: (1, 4)

Now, plot these points on a graph and draw a line through each set of points. The intersection will be the solution to the system of equations.

The solutions to the system of equations are x = 2 and y = 3.

Therefore, the system of equations is consistent and has a unique solution at (2, 3).