Solve the following system of equations by graphing. y = -x + 5 y = 2x - 4
To solve this system of equations by graphing, we need to plot the graphs of the two equations on the same coordinate plane and find their point of intersection.
First, graph the equation y = -x + 5:
1. Plot the y-intercept at (0, 5).
2. Use the slope of -1 to find the next point. From the y-intercept, move down 1 unit and right 1 unit to find the next point. Connect the two points with a straight line.
Next, graph the equation y = 2x - 4:
1. Plot the y-intercept at (0, -4).
2. Use the slope of 2 to find the next point. From the y-intercept, move up 2 units and right 1 unit to find the next point. Connect the two points with a straight line.
Now, you should have two lines on the same graph. The point where these two lines intersect is the solution to the system of equations. In this case, the lines intersect at the point (3, 2).
Therefore, the solution to the system of equations y = -x + 5 and y = 2x - 4 is x = 3 and y = 2.