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(Answer) MATH114N – Week 4 Assignment: Solving Systems of Linear Equations by Elimination

QUESTIONS

Question 1

The sum of two numbers is 155. Their difference is 23. Find the numbers.

Question 2

Decide whether it would be more convenient to solve the system of equations by substitution or elimination.

{−5x+14y=12

{7x+3y=4

  • elimination
  • substitution

Question 3

Solve the following system of equations:

{−x−6y=20

{−2x+5y=6

Question 4

Decide whether it would be more convenient to solve the system of equations by substitution or elimination.

{3x+8y = −13

{14x+3y/5 = −10

  • elimination
  • substitution

Question 5

Solve the following system of equations:

{−3x+4y=7

{7x−12y=−11

Question 6

The sum of two numbers is −17. Their difference is 41. Find the numbers.

Question 7

Solve the following system of equations:

{5x+4y = −20

{−7x−12y = −4

Question 8

Solve the following system of equations:

{−6x−y=2

{−7x−4y=−9

Write your answer as an ordered pair (x, y).

Question 9

Decide whether it would be more convenient to solve the system of equations by substitution or elimination.

{x/4 − 14y = 13

{−3x − 2y/3 = 7

  • elimination
  • substitution

Question 10

Decide whether it would be more convenient to solve the system of equations by substitution or elimination.

{−3x+3y= −12

{−6x+2y = 9

  • elimination
  • substitution

Question 11

Peter is buying office supplies. He is able to buy 3 packages of paper and 4 staplers for $40, or he is able to buy 5 packages of paper and 6 staplers for $62. How much does a package of paper cost? How much does a stapler cost?

Question 12

The total amount of sodium in 2 hot dogs and 3 cups of cottage cheese is 4,720mg. The total amount of sodium in 5 hot dogs and 2 cups of cottage cheese is 6,300mg. How much sodium is in a hot dog? How much sodium is in a cup of cottage cheese?

ANSWERS

Question 1

The sum of two numbers is 155. Their difference is 23. Find the numbers.

Answer: 89, 66​

Question 2

Decide whether it would be more convenient to solve the system of equations by substitution or elimination.

{−5x+14y=12

{7x+3y=4

  • elimination
  • substitution

Answer: elimination

Question 3

Solve the following system of equations:

{−x−6y=20

{−2x+5y=6

Answer: (−8, −2)​

Question 4….

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