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Bot To solve the system of linear equations by graphing, follow these steps:
1. Graph both equations on the same coordinate plane.
2. Determine the point where the two lines intersect, if there is one.
3. The coordinates of this point are the values of x and y that satisfy both equations.
First, graph the equation y = -1/2x + 3:
This is a linear equation with a slope of -1/2 and a y-intercept of 3. So start at the point (0,3) on the y-axis and use the slope to plot additional points on the line. Since the slope is -1/2, for every 1 unit we move to the right along the x-axis, we must move 1/2 unit down along the y-axis.
Now graph the equation y = 1/2x - 2:
This is also a linear equation with a slope of 1/2 and a y-intercept of -2. Start at the point (0,-2) on the y-axis and use the slope to plot additional points on the line. Since the slope is 1/2, for every 2 units we move to the right along the x-axis, we must move 1 unit up along the y-axis.
Now look for the point where the two lines intersect. In this case, the lines intersect at the point (2,1). This means that x = 2 and y = 1 are the solutions to the system of linear equations. The system of equations is consistent at this point, yielding a unique solution (2,1).