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Worksheet: Solving Systems of Nonlinear Equations Using Elimination

In this worksheet, we will practice solving a system of equations when both equations have like variables of the second degree.

Q1:

Find all the real solutions to the following system of equations

  • A π‘₯ = βˆ’ 3 and 𝑦 = βˆ’ 6 7
  • BThere are no solutions.
  • C π‘₯ = 9 and 𝑦 = βˆ’ 6 7
  • D π‘₯ = 3 and 𝑦 = 5
  • E π‘₯ = 6 and 𝑦 = βˆ’ 1 3

Q2:

Find all the real solutions to the system of equations

  • A π‘₯ = 4 and 𝑦 = 1 1
  • B π‘₯ = 2 or π‘₯ = βˆ’ 2 , 𝑦 = 1 or 𝑦 = 5
  • C π‘₯ = 4 or π‘₯ = βˆ’ 4 , 𝑦 = 3 or 𝑦 = 1 1
  • DThere are no solutions.
  • E π‘₯ = 1 6 and 𝑦 = βˆ’ 7

Q3:

Find all the real solutions to the system of equations:

  • A π‘₯ = βˆ’ 2 . 5 and 𝑦 = βˆ’ 5 . 9 3 7 5 , π‘₯ = 2 . 2 and 𝑦 = βˆ’ 1 0 . 9 9
  • BThere are no solutions.
  • C π‘₯ = βˆ’ 2 and 𝑦 = 7 , π‘₯ = 3 and 𝑦 = 1 0 . 7 5
  • D π‘₯ = βˆ’ 3 and 𝑦 = 4 . 7 5 , π‘₯ = 2 and 𝑦 = 1 1
  • E π‘₯ = βˆ’ 2 . 5 and 𝑦 = 5 . 9 3 7 5 , π‘₯ = 2 . 2 and 𝑦 = 1 1 . 2 9

Q4:

Find all the real solutions to the system of equations

  • A π‘₯ = 4 . 5 and 𝑦 = βˆ’ 3
  • BThere are no solutions.
  • C π‘₯ = 8 . 7 and 𝑦 = βˆ’ 5 . 2 5
  • D π‘₯ = 4 . 5 and 𝑦 = 0 . 7 5
  • E π‘₯ = 1 2 . 6 and 𝑦 = βˆ’ 2 1

Q5:

Find all the real solutions to the system of equations

  • A π‘₯ = 1 and 𝑦 = 0 , π‘₯ = 2 and 𝑦 = βˆ’ 6
  • BThere are no solutions.
  • C π‘₯ = βˆ’ 1 and 𝑦 = 0 , π‘₯ = 1 0 3 and 𝑦 = βˆ’ 2 6 9
  • D π‘₯ = βˆ’ 1 and 𝑦 = 0 , π‘₯ = 2 and 𝑦 = βˆ’ 6
  • E π‘₯ = 1 and 𝑦 = 0 , π‘₯ = βˆ’ 2 and 𝑦 = 6

Q6:

Find all the real solutions to the system of equations

  • A and
  • B and
  • C and
  • D and
  • E and

Q7:

Solve the simultaneous product equations Write each solution as an ordered pair ( π‘₯ , 𝑦 ) .

  • A(3, 4) and ο€Ό 2 4 , 1 2 
  • B(4, 3) and ο€Ό 2 4 , 1 2 
  • C ο€Ό 1 2 , 2 4 
  • D(3, 4) and ο€Ό 1 2 , 2 4 
  • E(4, 3)

Q8:

Solve the simultaneous product equations Write each solution as an ordered pair ( π‘₯ , 𝑦 ) .

  • A ( 2 , 3 )
  • B ( 3 , 2 ) and ο€Ό 1 2 , 1 2 
  • C ( 3 , 2 ) and ο€Ό 1 2 , 1 2 
  • D ( 2 , 3 ) and ο€Ό 1 2 , 1 2 
  • E ( 1 , 1 )

Q9:

Find all the real solutions to the system of equations

  • A π‘₯ = 0 and 𝑦 = 2 , π‘₯ = βˆ’ 7 and 𝑦 = 1 1 4
  • BThere are no solutions.
  • C π‘₯ = 0 and 𝑦 = 2 , π‘₯ = βˆ’ 0 . 6 and 𝑦 = 0 . 0 8
  • D π‘₯ = 0 𝑦 = 2 a n d , π‘₯ = βˆ’ 1 . 4 and 𝑦 = 0 . 8 8
  • E π‘₯ = 1 and 𝑦 = βˆ’ 2 , π‘₯ = βˆ’ 1 . 4 and 𝑦 = 0 . 8 8

Q10:

Find all the real solutions to the system of equations

  • A π‘₯ = βˆ’ 1 . 3 and 𝑦 = βˆ’ 2 . 5 8 , π‘₯ = βˆ’ 1 1 . 7 and 𝑦 = βˆ’ 6 4 . 2
  • B π‘₯ = βˆ’ 1 . 1 5 and 𝑦 = βˆ’ 1 . 2 4 5 , π‘₯ = βˆ’ 7 . 8 5 and 𝑦 = 9 7 . 7 9
  • C π‘₯ = βˆ’ 1 and 𝑦 = 6 , π‘₯ = 3 and 𝑦 = 1 2 6
  • DThere are no solutions.
  • E π‘₯ = βˆ’ 1 . 5 and 𝑦 = βˆ’ 4 . 5 , π‘₯ = βˆ’ 4 and 𝑦 = βˆ’ 4 2

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