This statement is false.
To solve the system of equations, y = -x + 3 and x + y = 8, we can graph the two equations on the same coordinate plane and find the point where they intersect, which represents the solution to the system.
Graphing the equation y = -x + 3 gives a straight line with a slope of -1 and a y-intercept of 3.
Graphing the equation x + y = 8 gives a straight line with a slope of -1 and a y-intercept of 8.
If we graph the two equations on the same coordinate plane, we find that the lines intersect at the point (2, 6). Therefore, there is a solution to the system, and the statement is false.
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.
3 answers
Does the graph show the system of equations x + y = 2 and −x + y = 7? Should the lines for the system be parallel?
No, the graph does not show the system of equations x + y = 2 and -x + y = 7. The correct system of equations should be x + y = 2 and -x + y = 7.
If we simplify the second equation, we get y = x + 7. This equation has a positive slope of 1, meaning that the line will go up as we move to the right. In contrast, the first equation y = -x + 2 has a negative slope of -1, meaning that the line will go down as we move to the right.
Since the slopes of the two lines are different, they cannot be parallel.
If we simplify the second equation, we get y = x + 7. This equation has a positive slope of 1, meaning that the line will go up as we move to the right. In contrast, the first equation y = -x + 2 has a negative slope of -1, meaning that the line will go down as we move to the right.
Since the slopes of the two lines are different, they cannot be parallel.