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The graphs represent this system: y=3x−2 −3x+y=7 How many solutions does this system have: 0, 1, or ∞ ?
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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 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 are parallel. The statement is true, because the lines are parallel. 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.
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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=7 is incorrect. The lines should be parallel. The graph of negative x plus y equals 7 is incorrect. 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. Both graphs are correct. The lines should be parallel. Both graphs are correct. The lines should be parallel. The graph of x+y=2 is incorrect. The lines should intersect.
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Solve the given system of linear equations by inspection.
y=3/5x−5
y= −3/5x−5

no solution
(0,−5)
infinitely many solutions
(−5,0)
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How do you find the solution to a system of equations graphically?(1 point) Responses Find the y-intercept of the two lines. Find the y-intercept of the two lines. Find the point where the two lines intersect. Find the point where the two lines intersect. Find the slope and y-intercept of the two lines. Find the slope and y-intercept of the two lines. Find the slope of the two lines. Find the slope of the two lines.
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What will the graph look like for a system of equations that has no solution?(1 point) Responses You will see the lines intersect at only one point. You will see the lines intersect at only one point. You will see lines on top of each other so that they form the same exact line. You will see lines on top of each other so that they form the same exact line. You will see parallel lines. You will see parallel lines. You will see perpendicular lines. You will see perpendicular lines. You will see the lines intersect at two different points. You will see the lines intersect at two different points.
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What will the graph look like for a system of equations that has no solution?(1 point) Responses You will see the lines intersect at only one point. You will see the lines intersect at only one point. You will see lines on top of each other so that they form the same exact line. You will see lines on top of each other so that they form the same exact line. You will see parallel lines. You will see parallel lines. You will see perpendicular lines. You will see perpendicular lines. You will see the lines intersect at two different points. You will see the lines intersect at two different points.

900 tickets are sold for the spring fling. Write an equation to represent this situation.
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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.

900 tickets are sold for the spring fling. Write an equation to represent this situation.
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Use the above system of equations to determine how many adult and student tickets were sold.
Answered by GPT 3.5
The given system of equations is:

y = 3x - 2
-3x + y = 7

To start, we can rearrange the second equation to solve for y:

-3x + y = 7
y = 3x + 7

Now we have the two equations:

y = 3x - 2
y = 3x + 7

From the equations, we can see that the slopes (coefficients of x) are the same (3) and the y-intercepts are different (-2 and 7). When the slopes are the same but the y-intercepts are different, the lines are parallel and do not intersect. Thus, this system has 0 solutions.
Answered by GPT 3.5
The statement is false, because the lines have an intersection point.

To solve the given system of equations:

y = -x + 3
x + y = 8

We can rearrange the second equation to solve for x:

x = 8 - y

Now we have the two equations:

y = -x + 3
x = 8 - y

From the equations, we can see that the slopes (coefficients of x) are different (-1 and 1) and the y-intercepts are different (3 and 8). When the slopes are different, the lines are not parallel and will intersect at a point. Thus, there is an intersection point and a solution to the system.
Answered by GPT 3.5
The graph of x+y=2 and −x+y=7 should have intersecting lines, not parallel lines.

The correct response is: The graph of −x+y=7 is incorrect. The lines should intersect.
Answered by GPT 3.5
By inspection, we can see that the equations have the same slope (-3/5) but different y-intercepts (-5 and -5). When the slopes are the same but the y-intercepts are different, the lines are parallel and do not intersect.

Therefore, the system of equations has no solution.
Answered by GPT 3.5
To find the solution to a system of equations graphically, you need to find the point where the two lines intersect.
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The graph for a system of equations that has no solution will show parallel lines.
Answered by GPT 3.5
Let x represent the number of tickets sold for the spring fling.

The equation to represent this situation would be: x = 900.
Answered by GPT 3.5
Let s represent the number of student tickets sold and a represent the number of adult tickets sold.

Given that adult tickets cost $4 and student tickets cost $2.50, we can write the equation:

4a + 2.50s = 2,820
Answered by GPT 3.5
Unfortunately, the information provided in the question is not sufficient to determine the exact number of adult and student tickets that were sold. We only have one equation (4a + 2.50s = 2,820) but not enough information to solve the system of equations. To find the values of a and s, we would need additional equations or information.