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Practice

2.3.5 Practice

2.3.5 • Practice

Complete the following questions to practice the skills you have learned in this lesson.

  1. Lin is solving this system of equations:

{ 6 x − 5 y = 34 3 x + 2 y = 8

She starts by rearranging the second equation to isolate the y variable: y = 4 − 1.5 x . She then substitutes the expression 4 − 1.5 x for y in the first equation, as shown:

6 x − 5 ( 4 − 1.5 x ) = 34
6 x − 20 − 7.5 x = 34

− 1.5 x = 54
x = − 36


y = 4 − 1.5 x

y = 4 − 1.5 ⋅ ( − 36 )

y = 58

Does Lin’s solution of ( − 36 , 58 ) makes both equations in the system true?

  1. No; Her solution does not make both equations true.
  2. yes; Her solution makes both equations true.
  1. Which of the following is true of Lin’s solution?
  1. Lin’s solution of ( − 36 , 58 ) is correct.
  2. Lin made an addition error. The correct answer is x = 0 and y = 4 , or ( 0 , 4 ) .
  3. Lin made a multiplication error. The correct answer is x = 9 and y = 4 , or ( 9 , 4 ) .
  4. Lin made a multiplication error. The correct answer is x = 4 and y = − 2 , or ( 4 , − 2 ) .

In questions 3 –9, solve the systems of equations by substitution.


  1. { 2 x + y = − 2 3 x − y = 7
  1. ( 2 , 6 )
  2. ( 1 , − 4 )
  3. ( 0 , − 2 )
  4. ( − 1 , 0 )
  1. { x − 3 y = − 9 2 x + 5 y = 4
  1. ( − 3 , 2 )
  2. ( 0 , 3 )
  3. ( 2 , 0 )
  4. ( − 6 , 1 )
  1. { − 2 x + 2 y = 6 2 y = − 6 x + 14
  1. ( − 3 , 0 )
  2. ( 2 , 1 )
  3. ( 0 , 7 )
  4. ( 1 , 4 )
  1. { 3 x + 4 y = 1 y = − 2 5 x + 2
  1. ( − 5 , 4 )
  2. ( − 1 , 1 )
  3. ( 0 , 2 )
  4. ( 5 , 0 )
  1. { 3 x + y = 10 x − 2 y = − 20
  1. ( 4 , 12 )
  2. ( − 4 , 8 )
  3. ( 0 , 10 )
  4. ( 2 , 2 )
  1. { y = x − 6 y = − 3 2 x + 4
  1. ( 0 , 4 )
  2. ( 4 , − 2 )
  3. ( 2 , 1 )
  4. ( 6 , 0 )
  1. { 2 x − 16 y = 8 − x − 8 y = − 4
  1. ( − 4 , − 1 )
  2. ( − 4 , 1 )
  3. ( 4 , 0 )
  4. ( 12 , 1 )
  1. { y = − 2 3 x + 6 2 x − y = 2
  1. ( 6 , 2 )
  2. ( 3 , 4 )
  3. ( − 2 , 0 )
  4. ( 0 , 6 )
  1. Tyler and Han are trying to solve this system by substitution:

{ x + 3 y = − 5 9 x + 3 y = 3

  • Tyler's first step is to isolate x in the first equation to get x = − 5 − 3 y .

  • Han's first step is to isolate 3y in the first equation to get 3 y = − 5 − x .

Solve using both methods to show that both first steps can be used to solve the system and will yield the same solution.

What is the solution to the system?

  1. ( − 5 , 0 )
  2. ( 4 , − 3 )
  3. ( 0 , 1 )
  4. ( 1 , − 2 )