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).

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

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).

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

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.

Tags

CCSS.HSA.CED.A.3

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.

Tags

CCSS.8.EE.C.8C

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.

Tags

CCSS.HSA.CED.A.3

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.

Tags

CCSS.8.EE.C.8B

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.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

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.

Tags

CCSS.8.EE.C.8B

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.

Tags

CCSS.8.EE.C.8B

CCSS.HSA.REI.C.6

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.