Determine If Statements Are True About Systems of Equations

The graph shows the system of which two equations?

At a concession stand, a pickle and two bags of chips costs a total of $3.25. Three pickles and four bags of chips costs a total of $7.25. To determine the cost of one pickle, Kevin is writing a system of equations. His first equation is shown: x + 2y = 3.25 Which of the following could be the second equation in his system of equations?

• 3x + 4y = 7.25

• 4x + 3y = 7.25

• 3x – 4y = 7.25

• 3 + 4)x = 7.25

What is the solution to this system of equations?

• (4, -1)

• (-1, 4)

• (-4, 1)

• (-4, -1)

Select two statements about the system of equations that are true.

• The system of equations has one solution.

• The two linear functions have the same rates of change.

• The system of equations has no solutions.

• The two linear functions have different rates of change.

• The system of equations has infinite solutions.

When graphed on the same coordinate plane, which equation results in a system of equations with exactly one solution?

• y = -2x+3

• y = -x+2

• y = -2x+3

• y = -2x + 4

Tickets to a movie cost $10 for adults, and $6 for children. A family purchased 5 tickets for $38. If x represents the number of adult tickets and y represents the number of children tickets, which system can be used to determine the number of adult and children tickets that were sold?

• x + 5 = y

  6x + 10y = 36

• x + y = 5

  10x + 6y = 38

• 5 + y = x

  10x + 38y = 6

• x + y = 5

  6x + 36y = 10

Which statement describes the solution(s) to the system of equations: -2x - 1y = 4 and -6x - 3y = 12?

• The system has a solution of (1,2).

• The system has a solution of (2,-4).

• The system has infinitely many solutions.

• The system has no solution.

Consider the system of equations: y = -2x - 5 x + 5y = -16 What is the solution to the system?

• (-2, 1)

• (4, -1)

• (-1, -3)

• (5, 1)

Two lines are graphed on the same coordinate plane. The lines intersect at the point (0,0). Which of these systems of linear equations could represent the two lines? Hint: Plugging in is a lot faster on this one than solving up to four systems.

• 3x + 3y = 9

  y = -6x - 9

• 5x + 1y = -13

  5x - 4y = 13

• -x - 4y = -4

  x + 2y = 4

• y = -3x

  2x - 5y = 0

Two equations of a system are listed. Which is a useful first step for solving the system?

• Substitute 2x from the second equation in for -4x in the first equation.

• Substitute 6y from the first equation in for 2x in the second equation.

• Substitute (2x - 3) from the second equation for y in the first equation.

• Substitute (-4x+6y) from the first equation for y in the second equation.