# Solving Systems by Elimination (Part 1)

ID: donub-duram
Illustrative Math
Subject: Algebra, Algebra 2

# Solving Systems by Elimination (Part 1)

Classroom:
Due:
Student Name:
Date Submitted:
##### Problem 1

1) Which equation is the result of adding these two equations?

﻿$\begin{cases} -2x + 4y = 17 \\ 3x - 10y = -3 \end{cases}$﻿

a) $-5x - 6y = 14$b) $-x - 6y = 14$c) $x - 6y = 14$d) $5x + 14y = 20$
##### Problem 2

2) Which equation is the result of subtracting the second equation from the first?

﻿$\begin{cases} 4x - 6y = 13 \\ -5x + 2y = 5 \end{cases}$﻿

a) $-9x - 4y = 8$b) $-x + 4y = 8$c) $x - 4y = 8$d) $9x - 8y = 8$
##### Problem 3

3) Solve this system of equations without graphing: ﻿$\begin{cases} 5x + 2y = 29 \\ 5x - 2y = 41 \end{cases}$﻿

Show Work
##### Problem 4

Here is a system of linear equations: ﻿$\begin{cases} 6x + 21y = 103 \\ -6x + 23y = 51 \end{cases}$﻿

4) Would you rather use subtraction or addition to solve the system?

##### Problem 5

6) Kiran sells ﻿$f$﻿ full boxes and ﻿$h$﻿ half-boxes of fruit to raise money for a band trip. He earns $5 for each full box and$2 for each half-box of fruit he sells and earns a total of \$100 toward the cost of his band trip. The equation ﻿$5f + 2h = 100$﻿ describes this relationship.

Solve the equation for ﻿$f$﻿.

Show Work
##### Problem 6

Match each equation with the corresponding equation solved for ﻿$a$﻿. Write the letter of the correct equation in each answer box.

a) ﻿$a = \frac{2b}{5} \quad \quad$﻿ b) ﻿$a = -\frac{2b}{5} \quad \quad$﻿ c) ﻿$a = -2b \quad \quad$﻿ d) ﻿$a = 2b - 5 \quad \quad$﻿ e) ﻿$a = 5 - 2b$﻿

7) ﻿$a + 2b = 5$﻿

8) ﻿$5a = 2b$﻿

9) ﻿$a + 5 = 2b$﻿

10) ﻿$5(a + 2b) = 0$﻿

11) ﻿$5a + 2b = 0$﻿

##### Problem 7

The volume of a cylinder is represented by the formula ﻿$V = \pi r^2 h$﻿.

Find the value of each labelled cell in the table.

﻿$\begin{array}{|c|c|c|} \hline \\[-1em] \textbf{volume (cubic inches)} & \textbf{radius (inches)} & \textbf{height (inches)} \\[-1em] \\ \hline \\[-1em] 96 \pi & 4 & \text{A} \\[-1em] \\ \hline \\[-1em] 31.25 \pi & 2.5 & \text{B} \\[-1em] \\ \hline \\[-1em] V & r & \text{C} \\[-1em] \\ \hline \end{array}$﻿

12) Cell A

13) Cell B

14) Cell C

##### Problem 8

Match each equation with the slope ﻿$m$﻿ and ﻿$y$﻿-intercept of its graph. Write the letter of the correct equation in each answer box.

a) ﻿$5x - 6y = 30 \quad \quad$﻿ b) ﻿$y = 5 - 6x \quad \quad$﻿ c) ﻿$y = \frac{5}{6}x + 1 \quad \quad$﻿ d) ﻿$5x - 6y = 6 \quad \quad$﻿ e) ﻿$5x + 6y = 6 \quad \quad$﻿ f) ﻿$6x + y = 12$﻿

15) ﻿$m = -6, \ y-\text{int} = (0,12)$﻿

16) ﻿$m = -6, \ y-\text{int} = (0,5)$﻿

17) ﻿$m = -\frac{5}{6}, \ y-\text{int} = (0,1)$﻿

18) ﻿$m = \frac{5}{6}, \ y-\text{int} = (0,1)$﻿

19) ﻿$m = \frac{5}{6}, \ y-\text{int} = (0,-1)$﻿

20) ﻿$m = \frac{5}{6}, \ y-\text{int} = (0,-5)$﻿

##### Problem 9

Solve each system of equations.

21) ﻿$\begin{cases} 2x + 3y = 4 \\ 2x = 7y + 24 \end{cases}$﻿

Show Work

22) ﻿$\begin{cases} 5x + 3y = 23 \\ 3y = 15x - 21 \end{cases}$﻿

Show Work
##### Problem 10

Elena and Kiran are playing a board game. After one round, Elena says, "You earned so many more points than I did. If you earned 5 more points, your score would be twice mine!"

Kiran says, "Oh, I don't think I did that much better. I only scored 9 points higher than you did."

23) Write a system of equations to represent each student's comment. Use the variables ﻿$k$﻿ and ﻿$e$﻿.

24) Specify what each variable represents.

25) If both students were correct, how many points did Elena score?