CPM Review Algebra Connections

Solve the following systems of equations using substitution:

2y + x = -15

x = 3y

• (-3, -9)

• (-9, -3)

• (-3, 9)

• (9, -3)

Answer explanation

Substitute x=3y into the first equation: 2y + 3y = -15. Simplify to get y=-3. Then substitute y=-3 into x=3y to find x=-9. Therefore, the solution is (-9, -3).

Solve the following systems of equations using substitution:

y = 3 - x

3y + x = 5

• No solution

• (1, 2)

• (3, 0)

• (2, 1)

Answer explanation

Substitute y = 3 - x into the second equation: 3(3-x) + x = 5. Solve for x to get x = 1. Then, substitute x = 1 back into y = 3 - x to find y = 2. Therefore, the solution is (1, 2).

Erin is 3 years younger than twice Alex's age. Their ages combined are 33 years. How old are Alex and Erin. If x=Erin's age and y=Alex's age, choose the system that matches the situation.

• x + y = 33
  y = 2x - 3

• x + y = 33
  x = 2y - 3

• x + y = 33
  x = 3 - 2y

• x + y = 3
  x = 33 - 2y

Answer explanation

The correct choice is x + y = 33 and x = 2y - 3 because Erin is 3 years younger than twice Alex's age, and their ages combined are 33 years. This system accurately represents the situation.

Nancy went to the grocery story. On Monday she purchased 4 apples and 6 bananas for a total of $13. On Wednesday she purchased 3 apples and 7 bananas for a total of $13.50. Which system of equations represents the situation?

• 4x + 6y = 3

  13.5x - 13y = 6

• x + y = 4

  x - y = 6

• 4x + 6y = 13

  3x + 7y = 13.5

• 4x - 6y = 13

  3x - 7y = 13.5

Answer explanation

The correct system of equations is 4x + 6y = 13 and 3x + 7y = 13.5, which represents the situation where Nancy purchased apples and bananas on Monday and Wednesday respectively.

The talent show committee sold a total of 530 tickets in advance. Student tickets cost $3 each and the adult tickets cost $4 each. If the total receipts were $1740, which system could be used to find how many of each type of ticket were sold?

• S + A = 530
  3S + 4A = 1740

• S + A = 530
  4S + 3A = 1740

• S + A = 1740
  3S + 4A = 530

• S + A = 1740
  4S + 3A = 530

Answer explanation

The correct choice is S + A = 530 and 3S + 4A = 1740 because it correctly represents the total number of tickets sold and the total receipts from selling student and adult tickets.

What is the solution to the system?

• (3, -1)

• (2, -6)

• No Solution 

• (6, -2)

Answer explanation

The correct solution to the system is (6, -2), as it satisfies both equations in the system.

The first step in solving using the substitution method is __________.

• get x by itself

• get y by itself

• get either variable by itself

• add the equations together

Answer explanation

To solve using the substitution method, the first step is to get either variable by itself.

The solution (x, y) to a system of equations is the point where they...? 

• Run off the graph

• Don't touch

• Intersect

• Exist

Answer explanation

The solution (x, y) to a system of equations is the point where they intersect.

Which is the best method to use?

• Graphing

• Substitution because a variable is isolated.

• Elimination because both equations are in standard form.

Answer explanation

Substitution because a variable is isolated.

Is (1,10) a solution to

y=7x+5

y=x+9

• yes

• no

Answer explanation

Substitute x=1 and y=10 into the equations to check. For y=7x+5, 10 is not equal to 7(1)+5. For y=x+9, 10 is not equal to 1+9. Therefore, (1,10) is not a solution.