Systems of Equations Mastery Quiz

• (1, 5)

• (-1, 1)

• (1, -1)

• No solution

Answer explanation

The solution to the system of equations is the point of intersection between the two lines, which is (1, 5). This is the correct choice.

Answer explanation

By adding the two equations, we eliminate y and solve for x. Substituting x back into one of the equations gives y. The solution is (2, 0).

• Infinite solutions

• No solution

Answer explanation

The system has infinite solutions because the two equations represent the same line. Any point on the line satisfies both equations.

Which graph represents a system of equations with no solution?

• Two intersecting lines

• Two parallel lines

• Two overlapping lines

• A line and a parabola that intersect

Answer explanation

Two parallel lines will never intersect, indicating no solution for the system of equations.

• No solution

Which graph represents a system of equations with an infinite number of solutions?

• Two intersecting lines

• Two parallel lines

• Two overlapping lines

• A line and a parabola that do not intersect

Answer explanation

Two overlapping lines represent a system of equations with an infinite number of solutions as they coincide with each other, indicating that every point on one line is also on the other line.

Write a system of equations for the following application: A total of 200 tickets were sold for a concert. Each adult ticket cost $25 and each child ticket costs $10. If the total revenue from ticket sales was $3,500 how many adult tickets and child tickets were sold?

Answer explanation

The correct choice is x + y = 200 and 25x + 10y = 3500 because it correctly represents the total number of tickets sold and the total revenue from ticket sales.

• No solution

Answer explanation

To solve by elimination, add the two equations to eliminate y. This results in x = 3. Substitute x back into one of the original equations to find y = 1. Therefore, the solution is (3, 1).

• No solution

Answer explanation

The solution is (2, 2) as it satisfies both equations when graphed.

Which graph represents a system of equations with exactly one solution?

• Two intersecting lines

• Two parallel lines

• Two overlapping lines

• A line and a parabola that do not intersect

Answer explanation

Two intersecting lines represent a system of equations with exactly one solution as they intersect at a single point.