Solving pairs of linear equations in two variables

The sum of two numbers is 86. The larger number is nine less than four times the smaller number.

What is the larger number?

• 19

• 67

• 86

• 15

Ben is 21 years older than Isaac. Three years ago, Ben was 4 times as old as Isaac.

How old is Ben now?

Mathematical Equivalence

ON

Tags

Solving System WP

Chelsea and Jennifer are selling wrapping paper for a school fundraiser. Customers can buy rolls of plain wrapping paper and rolls of shiny wrapping paper. Chelsea sold 12 rolls of plain

wrapping paper and 10 rolls of shiny wrapping paper for a total of $240. Jennifer sold 5 rolls of

plain wrapping paper and 5 rolls of shiny wrapping paper for a total of $115. Find the cost each of one roll of plain wrapping paper and one roll of shiny wrapping paper.

• roll of plain wrapping paper: $5, roll of shiny wrapping paper: $18

• roll of plain wrapping paper: $8, roll of shiny wrapping paper: $25

• roll of plain wrapping paper: $7, roll of shiny wrapping paper: $8

• roll of plain wrapping paper: $8, roll of shiny wrapping paper: $16

The senior class at Rivermont High School rented and filled 11 vans and 3 buses with 283 students. The senior class at Washington High School rented and filled 12 vans and 14 buses with 770 students. Which system of equations solves this problem to show how many students were in each van and each bus?

• 11v + 3b = 283

  12v + 14b = 770

• v + b = 14

  v + b = 16

• 11v + 12v = 283

  3b + 14b = 770

• v + b = 30

  23v + 17b = 1053

Nia sells pizzas. Large pizzas cost $8 each, and small pizzas cost $6 each. She sold 12 pizzas for $84. How many of each size pizza did Nia sell?

• 4 small and 8 large pizzas

• 5 small and 7 large pizzas

• 6 small and 6 large pizzas

• 10 small and 2 large pizzas

The volley club has 41 members. There are 3 more boys than girls. What are the two variables in the system?

• Members, Non-Members

• Boys, Girls

Homer sells tickets for admission to your school play and collects a total of $104. Admission prices are $6 for adults and $4 for children. He sold 21 tickets total.

To solve, I graphed:

x + y = 21 ,

6x + 4y = 104

I got an intersection point at (10,11). What does that mean in context of the problem?

• There are 10 adults and 11 children.

• There are 11 adults and 10 children.

• The adults are $10 and the children are $11.

• There are 104 adults and 21 children.

A 100-point test has x questions worth 2-points each and y questions worth 4 points each.

Which equation describes all possible numbers of questions that may be on the test?

• 2x + 4y = 100

• 4x + 2y = 100

• 2x = 4y

• 6xy = 100

Mike and Alejandro have a total of $213 together. Mike has $23 more than Alejandro. How much money do Mike and Alejandro each have?

• Mike=$118, Alejandro=$95

• Mike=$213, Alejandro=$190

• Mike=$170, Alejandro=$147

• Mike=$141, Alejandro=$72

There are 15 animals in a barn.  These animals are horses and chickens.  There are 44 legs in all.  Write a system of equations that could be used to determine the number of horses (x) and the number of chickens (y) in the barn.

• x + y = 15
  4x + 2y = 44
• 4x + 2y = 15
  x + y = 44
• x = 2y + 44
  4x = y + 15
• 2x - 4y = 44
  x - y = 15