se the image to answer the question. 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 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 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 false, because the lines have an intersection point. The image shows that the lines y=−x+3 and x+y=8 intersect at the point (2, 6), which means that there is a solution to the system.
One Solution, No Solution, or Many Solutions Quick Check 2 of 52 of 5 Items Question Use the image to answer the question. 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. 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 intersect. The graph of negative x plus y equals 7 is incorrect. The lines should intersect. The graph of −x+y=7 is incorrect. The lines should be parallel.
The graph of x+y=2 is incorrect. The lines should intersect.
One Solution, No Solution, or Many Solutions Quick Check 3 of 53 of 5 Items Question Which of these graphs shows that the linear system −2x+y=6 and 4x−2y=−12 has an infinite number of solutions?(1 point) Responses Image with alt text: A coordinate plane with 4 quadrants shows x and y axes ranging from negative 10 to 10 in unit increments. A line is plotted on the plane. An upward slanting line with arrows at both ends passes through the points left parenthesis 0 comma negative 6 right parenthesis and left parenthesis 3 comma 0 right parenthesis. Image with alt text: A coordinate plane with 4 quadrants shows x and y axes ranging from negative 10 to 10 in unit increments. A line is plotted on the plane. An upward slanting line with arrows at both ends passes through the points left parenthesis negative 3 comma 0 right parenthesis and left parenthesis 0 comma 6 right parenthesis. Image with alt text: A coordinate plane with 4 quadrants shows x and y axes ranging from negative 10 to 10 in unit increments. Two intersecting lines are plotted on the plane. A solid upward slanting line with arrows at both ends passes through the points left parenthesis negative 3 comma 0 right parenthesis and left parenthesis 0 comma 6 right parenthesis. A dotted upward slanting line passes through the points left parenthesis 0 comma 6 right parenthesis and left parenthesis 1 comma 7 right parenthesis. Image with alt text: A coordinate plane with 4 quadrants shows x and y axes ranging from negative 10 to 10 in unit increments. Two parallel lines are plotted on the plane. A dotted upward slanting line with arrows at both ends passes through the points left parenthesis negative 3 comma 0 right parenthesis and left parenthesis 0 comma 6 right parenthesis. A solid upward slanting line with arrows at both ends, parallel to the dotted line, passes through origin. Skip to navigation
The correct response is: Image with alt text: A coordinate plane with 4 quadrants shows x and y axes ranging from negative 10 to 10 in unit increments. Two intersecting lines are plotted on the plane. A solid upward slanting line with arrows at both ends passes through the points left parenthesis negative 3 comma 0 right parenthesis and left parenthesis 0 comma 6 right parenthesis. A dotted upward slanting line passes through the points left parenthesis 0 comma 6 right parenthesis and left parenthesis 1 comma 7 right parenthesis. This graph shows that the linear system −2x+y=6 and 4x−2y=−12 has an infinite number of solutions.
Which of these graphs shows that the linear system y=−x+6 and 3x+3y=18 has an infinite number of solutions?(1 point) Responses Image with alt text: A coordinate plane with 4 quadrants shows x and y axes ranging from negative 10 to 10 in unit increments. A line is plotted on the plane. A downward slanting line with arrows at both ends passes through the points left parenthesis 0 comma 6 right parenthesis and left parenthesis 6 comma 0 right parenthesis. Image with alt text: A coordinate plane with 4 quadrants shows x and y axes ranging from negative 10 to 10 in unit increments. Two parallel lines are plotted on the plane. A solid downward slanting line with arrows at both ends passes through the points left parenthesis 0 comma 6 right parenthesis and left parenthesis 6 comma 0 right parenthesis. A dotted downward slanting line with arrows at both ends passes through the points left parenthesis 0 comma 4 right parenthesis and left parenthesis 4 comma 0 right parenthesis. Image with alt text: A coordinate plane with 4 quadrants shows x and y axes ranging from negative 10 to 10 in unit increments. A line is plotted on the plane. A downward slanting line with arrows at both ends passes through the points left parenthesis negative 6 comma 0 right parenthesis and left parenthesis 0 comma negative 6 right parenthesis. Image with alt text: A coordinate plane with 4 quadrants shows x and y axes ranging from negative 10 to 10 in unit increments. Two intersecting lines are plotted on the plane. A solid downward slanting line with arrows at both ends passes through the points left parenthesis 0 comma 6 right parenthesis and left parenthesis 6 comma 0 right parenthesis. A dotted downward slanting line with arrows at both ends passes through the points left parenthesis negative 6 comma 4 right parenthesis and left parenthesis 3 comma 3 right parenthesis. Skip to navigation
The correct response is: Image with alt text: A coordinate plane with 4 quadrants shows x and y axes ranging from negative 10 to 10 in unit increments. Two intersecting lines are plotted on the plane. A solid downward slanting line with arrows at both ends passes through the points left parenthesis 0 comma 6 right parenthesis and left parenthesis 6 comma 0 right parenthesis. A dotted downward slanting line with arrows at both ends passes through the points left parenthesis negative 6 comma 4 right parenthesis and left parenthesis 3 comma 3 right parenthesis. This graph shows that the linear system y=−x+6 and 3x+3y=18 has an infinite number of solutions.
One Solution, No Solution, or Many Solutions Quick Check 5 of 55 of 5 Items Question Solve the given system of linear equations by inspection. y=3/5x−5 y=−3/5x−5 (1 point) Responses (0,−5) left parenthesis 0 comma negative 5 right parenthesis (−5,0) left parenthesis negative 5 comma 0 right parenthesis infinitely many solutions infinitely many solutions no solution
The correct response is "infinitely many solutions". By visually inspecting the equations, you can see that both equations have the same slope (-3/5) and the same y-intercept (-5), meaning they are the same line, and therefore have an infinite number of solutions.
The statement is false, because the lines have an intersection point.
To solve the system of equations y = -x + 3 and x + y = 8 by graphing, we can draw the graphs of both equations on a coordinate plane.
To graph the first equation y = -x + 3, we can start by assigning values to x and finding the corresponding values of y. For example, when x = 0, y = -0 + 3 = 3. When x = 1, y = -1 + 3 = 2. We can continue this process to find more points and connect them to create a line.
To graph the second equation x + y = 8, we can rearrange it to y = -x + 8. Again, we can assign values to x and find the corresponding values of y. For example, when x = 0, y = -0 + 8 = 8. When x = 1, y = -1 + 8 = 7. We can find more points and connect them to create another line.
Now, we can plot both lines on the same coordinate plane. After drawing the lines for both equations, we can see that they intersect at a point (2, 6). This means that there is a solution to the system of equations.
Therefore, the statement is false because it claims that there is no solution to the system, but in fact, there is an intersection point between the lines.