solve the following system of equations graphically on the set of axes below. \n$y = -\\frac{1}{2}x + 2$\n$x…

Explanation:

Step1: Analyze the first equation ( y = -\frac{1}{2}x + 2 )

To graph this line, we can find the ( y )-intercept and the slope. The ( y )-intercept (( b )) is 2, so the point ( (0, 2) ) is on the line. The slope (( m )) is ( -\frac{1}{2} ), which means from the ( y )-intercept, we can go down 1 unit and right 2 units to find another point, e.g., ( (2, 1) ), ( (4, 0) ), etc.

Step2: Analyze the second equation ( x - y = 1 )

Rewrite it in slope - intercept form (( y=mx + b )): ( x - y=1) can be rewritten as ( y=x - 1 ). The ( y )-intercept is ( - 1 ), so the point ( (0,-1) ) is on the line. The slope is 1, which means from the ( y )-intercept, we can go up 1 unit and right 1 unit to find another point, e.g., ( (1,0) ), ( (2,1) ), etc.

Step3: Find the intersection point

By plotting the two lines (either by using the points we found or by using a graphing tool), we look for the point where the two lines cross each other. From the equations, we can also solve the system algebraically to verify. Substitute ( y = x - 1 ) into ( y=-\frac{1}{2}x + 2 ): ( x - 1=-\frac{1}{2}x+2) Add ( \frac{1}{2}x ) to both sides: ( x+\frac{1}{2}x-1 = 2) ( \frac{3}{2}x-1=2) Add 1 to both sides: ( \frac{3}{2}x=3) Multiply both sides by ( \frac{2}{3} ): ( x = 2) Substitute ( x = 2 ) into ( y=x - 1 ), we get ( y=2 - 1=1 )

Answer:

The solution to the system of equations is ( x = 2 ), ( y = 1 ) or the ordered pair ( (2,1) )