Question

Solve by graphing
y = -x + 5
y = 2x - 4

Answer 1

To solve by graphing, we need to graph both equations on the same coordinate plane and find the point of intersection. This point will represent the solution to the system of equations.

Let's start by graphing the first equation y = -x + 5:
To graph y = -x + 5, we need to plot the y-intercept at (0, 5) and then use the slope (-1) to find additional points. So, we can plot a point at (0, 5) and then move down 1 unit and right 1 unit to get another point, connect the points to draw the line.

Now let's graph the second equation y = 2x - 4:
To graph y = 2x - 4, we need to plot the y-intercept at (0, -4) and then use the slope (2) to find additional points. So, we can plot a point at (0, -4) and then move up 2 units and right 1 unit to get another point, connect the points to draw the line.

Now we have both lines plotted on the same coordinate plane. The point where the two lines intersect is the solution to the system of equations y = -x + 5 and y = 2x - 4.

The point of intersection is (3, 2). This means that x = 3 and y = 2 is the solution to the system of equations.

Therefore, the solution to the system of equations is x = 3 and y = 2.