Use the image to answer the question.
A coordinate plane with 4 quadrants ranges from negative 10 to 10 in unit increments on both the x and y axes. A solid line and a dashed line with arrows at both the ends are drawn parallel to each other on the graph. The equation of the solid line is y equals negative x plus 3. The equation of the dashed line is x plus y equals 8.
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.
(1 point)
Responses
The statement is true, because the lines have an intersection point.
The statement is true, because the lines have an intersection point.
The statement is false, because the lines are parallel.
The statement is false, because the lines are parallel.
The statement is true, because the lines are parallel.
The statement is true, because the lines are parallel.
The statement is false, because the lines have an intersection point.
The statement is false, because the lines have an intersection point.
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The statement is false, because the lines have an intersection point.
From the given information, we know that the solid line has an equation of y = -x + 3 and the dashed line has an equation of x + y = 8.
To solve the system of equations by graphing, we can plot the two lines on the coordinate plane.
The solid line y = -x + 3 has a y-intercept of 3 and a slope of -1. The dashed line x + y = 8 can be rewritten as y = -x + 8, and it also has a y-intercept of 8 and a slope of -1.
When we plot these lines on the coordinate plane, we can see that they intersect at the point (2, 6). Therefore, there is a solution to the system and the statement is false.
Is it a b c or d
The correct answer is d. The statement is false, because the lines have an intersection point.
The statement is false, because the lines are parallel. The solid line and the dashed line in the coordinate plane are shown as parallel lines and they do not intersect each other. Therefore, there is no solution to the system y = −x + 3 and x + y = 8.
To answer this question, we need to consider the equations of the two lines and analyze their relationship on the graph.
The equation of the solid line is y = -x + 3. This equation represents a straight line with a slope of -1 and a y-intercept of 3. The line slants downwards from left to right.
The equation of the dashed line is x + y = 8. This equation can be rewritten in slope-intercept form as y = -x + 8. This line also has a slope of -1, but its y-intercept is 8. The line slants downwards from right to left.
To graph these lines, we can locate and plot a few points on each line. For the solid line, we can start at the y-intercept of 3 and use the slope of -1 to plot additional points. For the dashed line, we can start at the y-intercept of 8 and again use the slope of -1 to plot more points. Once we have enough points, we can connect them with straight lines.
After graphing these lines, we can observe that they are parallel to each other. They do not intersect at any point on the coordinate plane. Therefore, the statement that "there is no solution to the system" is true.
Hence, the correct answer is: The statement is true, because the lines are parallel.