solving the system y = -x + 3 and x + y = 8 by graphing shows that there is no solution to the system. is this statement true or false? explain.

Answer 1

This statement is false.

To solve the system y = -x + 3 and x + y = 8 by graphing, we can plot the two equations on a graph. The first equation y = -x + 3 is a straight line with a y-intercept of 3 and a slope of -1. The second equation x + y = 8 is also a straight line with a y-intercept of 8 and a slope of -1.

When we graph both equations on the same coordinate plane, we can see that the two lines intersect at the point (2, 6). This means that there is a unique solution to the system of equations, contradicting the initial statement that there is no solution.

Answer 2

so
A. the statement is false, because the lines have an intersection point.
B. The statement is false, because the lines are parallel.
which one?

Answer 3

A. the statement is false, because the lines have an intersection point.

Answer 4

does the graph show the system of equations x + y = 2 and -x + y = 7? should the lines for the system be parallel?

Answer 5

Yes, the graph shown represents the system of equations x + y = 2 and -x + y = 7.

The equations can be rewritten in slope-intercept form as y = -x + 2 and y = x + 7, respectively. From the slope-intercept form, we can see that the slopes of the two equations are -1 and 1, respectively. Since the slopes are different, the lines should not be parallel.

When graphed, you will see that the two lines intersect at the point (-4.5, 6.5), showing that a unique solution exists for this system of equations.