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)
This statement is false.
To solve the system by graphing, we need to graph the two equations on the same coordinate plane and find the point(s) where the graphs intersect. If the graphs intersect at a point, that point represents the solution to the system.
For the first equation, y = -x + 3, we can start by finding the intercepts. When x equals 0, y = -0 + 3, so one point on the graph is (0, 3). When y equals 0, 0 = -x + 3, so x = 3, giving us another point (3, 0). Plotting these two points and connecting them with a line, we get the graph for the first equation.
For the second equation, x + y = 8, we can also find the intercepts. When x equals 0, 0 + y = 8, so y = 8, giving us the point (0, 8). When y equals 0, x + 0 = 8, so x = 8, giving us another point (8, 0). Plotting these two points and connecting them with a line, we get the graph for the second equation.
By graphing both equations, we see that the graphs intersect at the point (2, 6). This point represents the solution to the system. Therefore, the statement is false.
The statement is false, 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 true, because the lines have an intersection point.
The statement is false, because the lines have an intersection point.
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.
Both graphs are correct. The lines should be parallel.
The graph of −x+y=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.
Solve the given system of linear equations by inspection.
y=3/5x−5
y=−3/5x −5 (1 point)
Answer Choices:
no solution
(0,−5)
(−5,0)
infinitely many solutions
To solve the given system of linear equations by inspection, we can observe that both equations have the same slope of -3/5 and the same y-intercept of -5. This indicates that the two lines are parallel and will never intersect. Therefore, the correct answer is no solution.
How do you find the solution to a system of equations graphically?(1 point)
Responses-
Find the slope and y-intercept of the two lines.
Find the slope of the two lines.
Find the y-intercept of the two lines.
Find the point where the two lines intersect.
To find the solution to a system of equations graphically, you need to find the point where the two lines intersect.
Georgia Connections Academy is selling tickets to its Spring Fling. Adult tickets cost $4 and student tickets cost $2.50. The school makes $2,820. Write an equation that represents this situation to find the cost of all adult and student tickets sold. Use the variable s for student tickets and a for adult tickets sold. (7 points)
Write an equation that represents this situation to find the cost of all adult and student tickets sold. Use the variable s for student tickets and a for adult tickets sold: ____ a + ____ s = ____
900 tickets are sold for the spring fling. Write an equation to represent this situation: a+ ____ =____
Use the above system of equations to determine how many adult and student tickets were sold: ___adult tickets and___ student tickets were sold.