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=8a by graphing shows that there is no solution to the system. Is this statement true or false? Explain. (1 point) Responses The statement is false, because the lines have an intersection point. The statement is false, because the lines have an intersection point. 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 true, because the lines are parallel. The statement is true, because the lines are parallel. 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 equation of the solid line y = -x + 3 has a slope of -1, which means it is a downward-sloping line.
The equation of the dashed line x + y = 8 can be rearranged to y = -x + 8, which also has a slope of -1 and is a downward-sloping line.
Since the slopes of both lines are the same (-1), the lines are parallel and do not intersect. Therefore, there is no solution to the system of equations.
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 solid line passes through left parenthesis 0 comma 2 right parenthesis and left parenthesis 2 comma 0 right parenthesis. The dashed line passes through left parenthesis negative 7 comma 0 right parenthesis and left parenthesis 7 comma 0 right parenthesis.
Does the graph show the system of equations x+y=2 and −x+y=7 ? Should the lines for the system be parallel? (1 point) Responses The graph of x+y=2 is incorrect. The lines should intersect. The graph of x plus y equals 2 is incorrect. The lines should intersect. The graph of −x+y=7 is incorrect. The lines should intersect. The graph of negative x plus y equals 7 is incorrect. The lines should intersect. Both graphs are correct. The lines should be parallel. Both graphs are correct. The lines should be parallel. The graph of −x+y=7 is incorrect. The lines should be parallel.
The graph shows the system of equations x+y=2 and −x+y=7.
The solid line passes through the points (0,2) and (2,0), which satisfies the equation x+y=2.
The dashed line passes through the points (-7,0) and (7,0), which satisfies the equation −x+y=7 when it is rearranged to y=x+7.
Since both lines satisfy their respective equations, the graph shows the system of equations x+y=2 and −x+y=7.
The lines should not be parallel, as they intersect at the point (2,0), where both equations are satisfied. Therefore, the statement "The lines should be parallel" is incorrect.
The correct response is: The graph of −x+y=7 is incorrect. The lines should intersect.
The statement is false, because the lines have an intersection point.
To solve the system of equations y = -x + 3 and x + y = 8, we can graph the equations and find where they intersect.
First, let's graph the equation y = -x + 3. We start by plotting a point at (0, 3), since when x = 0, y = 3. Then, we can find more points by selecting various x-values and substituting them into the equation to find the corresponding y-values. For example, when x = 1, y = -1 + 3 = 2, so we plot the point (1, 2). By connecting these points, we can draw the solid line.
Next, let's graph the equation x + y = 8. We start by finding the x and y-intercepts. When y = 0, x = 8, so we plot the point (8, 0). When x = 0, y = 8, so we plot the point (0, 8). By connecting these points, we can draw the dashed line.
Upon graphing the two lines, we can clearly see that they intersect at the point (2, 6). Therefore, the statement that there is no solution to the system is false, as the lines do indeed have an intersection point.
The statement is true because the lines are parallel.
To determine if two equations have a solution, we can graph them on the coordinate plane and see if they intersect. In this case, the solid line has the equation y = -x + 3 and the dashed line has the equation x + y = 8.
To graph the solid line, we can start by finding two points on the line. We can choose any values for x and substitute them into the equation to find the corresponding y-values. For example, when x = 0, y = -0 + 3 = 3. So one point on the line is (0, 3). Similarly, when x = 2, y = -2 + 3 = 1. So another point on the line is (2, 1). Plotting these points on the coordinate plane and drawing a straight line through them gives us the solid line.
To graph the dashed line, we can rearrange the equation x + y = 8 to y = -x + 8. Again, we can choose values for x and find the corresponding y-values. For example, when x = 0, y = -0 + 8 = 8. So one point on the line is (0, 8). When x = 2, y = -2 + 8 = 6. So another point on the line is (2, 6). Plotting these points and drawing a straight line gives us the dashed line.
Upon examining the graph, we can see that the solid line and the dashed line are parallel and do not intersect. Therefore, there is no solution to the system of equations. Thus, the statement is true because the lines are parallel.