Unit 4 Lesson 3 Solving Systems with Linear Combinations 1

Elliot has a total of 26 books. He has 12 more fiction books than nonfiction books. Let x represent the number of fiction books. Which equation represents the situation?

• $x=x+12$

• $x+\left(x-12\right)=26$

• $x+\left(x+12\right)=26$

Elliot has a total of 26 books. He has 12 more fiction books than nonfiction books. Let x represent the number of fiction books. How many fiction books does Elliot have?

• 7

• 12

• 19

Elliot has a total of 26 books. He has 12 more fiction books than nonfiction books. Let x represent the number of fiction books. How many nonfiction books does Elliot have?

• 7

• 12

• 19

Elliot has a total of 26 books. He has 12 more fiction books than nonfiction books. Let x represent the number of fiction books and y represent the number of nonfiction books. Which system of linear equations represents the situation?

• x + y = 26 and x + y = 12

• x + y = 26 and x – y = 12

• x + y = 26 and –x + y = 12

• x – y = 26 and x + y = 12

Elliot has a total of 26 books. He has 12 more fiction books than nonfiction books. Let x represent the number of fiction books and y represent the number of nonfiction books.

This system of equations models the number of books.

x + y = 26

x – y = 12

Elliot added the two equations and the result was 2x = 38.

Solve the equation. How many fiction books does Elliot have? (Just write the number answer)

Elliot has a total of 26 books. He has 12 more fiction books than nonfiction books. Let x represent the number of fiction books and y represent the number of nonfiction books.

This system of equations models the number of books.

x + y = 26

x – y = 12

Elliot added the two equations and the result was 2x = 38. How many nonfiction books does Elliot have?

Use this system of equations to answer the questions that follow.

4x – 9y = 7

–2x + 3y = 4

What number would you multiply the second equation by in order to eliminate the x-terms when adding to the first equation?

Use this system of equations to answer the questions that follow.

4x – 9y = 7

–2x + 3y = 4

What number would you multiply the second equation by in order to eliminate the y-terms when adding to the first equation?

An equivalent equation has been written by multiplying the second equation by 2.

4x – 9y = 7 → 4x – 9y = 7

2(–2x + 3y = 4) → –4x + 6y = 8

What is the solution to the system?

• $\left(-\frac{19}{2},\ -5\right)$

• $\left(-5,\ -\frac{19}{2}\right)$

• $\left(-\frac{15}{2},-\frac{11}{3}\right)$

• $\left(-\frac{19}{10},\ \frac{1}{15}\right)$

The drama club is selling short-sleeved shirts for $5 each, and long-sleeved shirts for $10 each. They hope to sell all of the shirts they ordered, to earn a total of $1,750. After the first week of the fundraiser, they sold of the short-sleeved shirts and of the long-sleeved shirts, for a total of 100 shirts.

Let x represent the number of short-sleeved shirts ordered and let y represent the number of long-sleeved shirts ordered. Which system of linear equations represents the situation?

• $5x+10y=100\ \ AND\ \frac{1}{3}x+\frac{1}{2}y=1750$

• $5x+10y=1750\ AND\ \frac{1}{3}x+\frac{1}{2}y=100$

• $x+y=100\ \ AND\ \frac{1}{3}x+\frac{1}{2}y=1750$

• $x+y=1750\ AND\ \frac{1}{3}x+\frac{1}{2}y=100$