question\nsolve the following system of equations graphically on the set of axes below.\n$y = 3x - 8$\n$y =…

Explanation:

Step1: Analyze ( y = 3x - 8 )

Find two points. When ( x = 0 ), ( y = 3(0) - 8 = -8 ), so point ((0, -8)). When ( x = 2 ), ( y = 3(2) - 8 = -2 ), so point ((2, -2)). Plot these and draw the line.

Step2: Analyze ( y = -2x - 3 )

Find two points. When ( x = 0 ), ( y = -2(0) - 3 = -3 ), so point ((0, -3)). When ( x = 1 ), ( y = -2(1) - 3 = -5 ), so point ((1, -5)). Plot these and draw the line.

Step3: Find Intersection

The lines intersect where ( 3x - 8 = -2x - 3 ). Solve: ( 3x + 2x = -3 + 8 ) → ( 5x = 5 ) → ( x = 1 ). Substitute ( x = 1 ) into ( y = 3x - 8 ): ( y = 3(1) - 8 = -5 )? Wait, no, wait: ( 3x - 8 = -2x - 3 ) → ( 5x = 5 ) → ( x = 1 ). Then ( y = 3(1) - 8 = -5 )? Wait, no, ( y = -2(1) - 3 = -5 ). Wait, earlier when ( x = 1 ) for ( y = -2x - 3 ), ( y = -5 ), and for ( y = 3x - 8 ), when ( x = 1 ), ( y = -5 ). Wait, but when ( x = 2 ) for ( y = 3x - 8 ), ( y = -2 ). Wait, maybe better to solve algebraically first. Set ( 3x - 8 = -2x - 3 ): ( 3x + 2x = -3 + 8 ) → ( 5x = 5 ) → ( x = 1 ), then ( y = 3(1) - 8 = -5 ). So the intersection is ((1, -5)). But graphically, plot the two lines: ( y = 3x - 8 ) has slope 3, y-intercept -8; ( y = -2x - 3 ) has slope -2, y-intercept -3. The intersection is at ((1, -5)).

Answer:

The solution (intersection point) is ((1, -5)). To graph: plot ( y = 3x - 8 ) through ((0, -8)) and ((2, -2)), plot ( y = -2x - 3 ) through ((0, -3)) and ((1, -5)), and the lines intersect at ((1, -5)).