﻿ Solve System of Equations Worksheet | Problems & Solutions

Solve System of Equations Worksheet

Solve System of Equations Worksheet
• Page 1
1.
Find the value of $a$ for the given dependent system.
$y$ = 6$x$ + $a$
24$x$ - 4$y$ = 36
 a. 37 b. - 9 c. 4 d. 36

2.
Use the elimination method to solve the system:
8$x$ + $y$ = 8$z$ - 1
$x$ - $z$ = - 1
57$x$ + 8 = $y$ - 7$z$
 a. ($\frac{1}{8}$, 7, - $\frac{7}{8}$) b. (- $\frac{1}{8}$, 0, $\frac{7}{8}$) c. (- $\frac{1}{8}$, 7, $\frac{7}{8}$) d. ($\frac{1}{8}$, 0, - $\frac{7}{8}$)

3.
John has some chocolates and books. The number of chocolates he has is equal to 6 times the number of books. If the sum of the chocolates and twice the number of books is 16, find the number of chocolates and books.
 a. 4, 24 b. 1, 10 c. 3, 14 d. 12, 2

4.
Solve the system using the elimination method:
$\frac{x}{16}$ + $\frac{y}{15}$ = 35
$\frac{x}{3}$ - $\frac{z}{16}$ = - 1
5$x$ - $\frac{y}{3}$ = 80
 a. (48, 480, 272) b. (51, 480, 240) c. (51, 570, 272) d. (48, 570, 240)

5.
State whether the system is consistent and independent, consistent and dependent or inconsistent using the elimination method.
9$x$ + $y$ = 10
$y$ - 9$z$ = 82
10$x$ + 10$z$ = - 80
 a. Inconsistent b. Cannot be determined c. Consistent and dependent d. Consistent and independent

6.
State whether the system is consistent and independent, consistent and dependent or inconsistent using the elimination method.
$x$ - 11$y$ - 120$z$ = - 122
11$x$ + $y$ = 100$z$
10$x$ + 30$z$ = 133 - 13$y$
 a. Cannot be determined b. Inconsistent c. Consistent and dependent d. Consistent and independent

7.
A company makes pens, batteries, and soaps. A pack consisting of 3 pens and 1 soap costs $40, a pack consisting of 1 battery and 1 soap costs$28 and a pack consisting of 1 pen and 1 battery costs $20. Find the cost of a pen, a battery and a soap using the elimination method.  a. ($16, $36,$8) b. ($8,$12, $16) c. ($40, $28,$20) d. ($22,$42, \$70)

8.
Out of two numbers, the larger number is equal to 10 plus double the smaller number. If the larger number is greater than the smaller number by 10, then find the numbers using the graphical method.
 a. 2, 12 b. 4, 14 c. 0, 10 d. 5, 15

9.
Solve the linear system:
$x$ - 5$y$ = 8 --- (1)
- 5$x$ + 6$y$ = -2 --- (2)
 a. (- 2 , - 2) b. (2 , 2) c. (2 , - 2) d. (- 2 , 2)

- 10$x$ + 9$y$ = - 45
9$y$ = 9 + 8$x$