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 𝑦 = 2 𝑥 + 1 2 𝑥 1 3 , 𝑦 = 𝑥 3 + 2 𝑥 + 2 .

  • A 𝑥 = 3 and 𝑦 = 6 7
  • B 𝑥 = 6 and 𝑦 = 1 3
  • C 𝑥 = 9 and 𝑦 = 6 7
  • D 𝑥 = 3 and 𝑦 = 5
  • EThere are no solutions.

Q2:

Find all the real solutions to the system of equations 3 𝑦 𝑥 + 3 𝑥 + 5 = 0 , 2 𝑦 𝑥 + 𝑥 + 1 = 0 .

  • A 𝑥 = 2 or 𝑥 = 2 , 𝑦 = 1 or 𝑦 = 5
  • B 𝑥 = 4 or 𝑥 = 4 , 𝑦 = 3 or 𝑦 = 1 1
  • C 𝑥 = 1 6 and 𝑦 = 7
  • DThere are no solutions.
  • E 𝑥 = 4 and 𝑦 = 1 1

Q3:

Find all the real solutions to the system of equations: 4 𝑦 + 𝑥 4 𝑥 4 0 = 0 , 2 𝑦 7 2 𝑥 6 𝑥 + 4 = 0 .

  • AThere are no solutions.
  • B 𝑥 = 3 and 𝑦 = 4 . 7 5 , 𝑥 = 2 and 𝑦 = 1 1
  • C 𝑥 = 2 . 5 and 𝑦 = 5 . 9 3 7 5 , 𝑥 = 2 . 2 and 𝑦 = 1 1 . 2 9
  • D 𝑥 = 2 . 5 and 𝑦 = 5 . 9 3 7 5 , 𝑥 = 2 . 2 and 𝑦 = 1 0 . 9 9
  • E 𝑥 = 2 and 𝑦 = 7 , 𝑥 = 3 and 𝑦 = 1 0 . 7 5

Q4:

Find all the real solutions to the system of equations 5 𝑦 𝑥 + 9 𝑥 2 4 = 0 , 3 𝑦 + 𝑥 9 𝑥 + 1 8 = 0 .

  • A 𝑥 = 1 2 . 6 and 𝑦 = 2 1
  • BThere are no solutions.
  • C 𝑥 = 4 . 5 and 𝑦 = 0 . 7 5
  • D 𝑥 = 8 . 7 and 𝑦 = 5 . 2 5
  • E 𝑥 = 4 . 5 and 𝑦 = 3

Q5:

Find all the real solutions to the system of equations y = x y = 2 x 3 𝑥 4 , 4 𝑥 6 .

  • A 𝑥 = 1 and 𝑦 = 0 , 𝑥 = 2 and 𝑦 = 6
  • B 𝑥 = 1 and 𝑦 = 0 , 𝑥 = 1 0 3 and 𝑦 = 2 6 9
  • CThere are no solutions.
  • D 𝑥 = 1 and 𝑦 = 0 , 𝑥 = 2 and 𝑦 = 6
  • E 𝑥 = 1 and 𝑦 = 0 , 𝑥 = 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 𝑥 𝑦 = 1 2 , ( 𝑥 1 ) ( 𝑦 8 ) = 8 . Write each solution as an ordered pair ( 𝑥 , 𝑦 ) .

  • A(3, 4) and 2 4 , 1 2
  • B 1 2 , 2 4
  • C(4, 3)
  • D(4, 3) and 2 4 , 1 2
  • E(3, 4) and 1 2 , 2 4

Q8:

Solve the simultaneous product equations 𝑥 𝑦 = 6 , ( 𝑥 1 ) ( 𝑦 6 ) = 3 . Write each solution as an ordered pair ( 𝑥 , 𝑦 ) .

  • A ( 2 , 3 ) and 1 2 , 1 2
  • B ( 1 , 1 )
  • C ( 2 , 3 )
  • D ( 3 , 2 ) and 1 2 , 1 2
  • E ( 3 , 2 ) and 1 2 , 1 2

Q9:

Find all the real solutions to the system of equations 𝑦 = 3 𝑥 + 5 𝑥 + 2 , 𝑦 = 2 𝑥 2 𝑥 + 2 .

  • A 𝑥 = 0 and 𝑦 = 2 , 𝑥 = 0 . 6 and 𝑦 = 0 . 0 8
  • BThere are no solutions.
  • C 𝑥 = 0 and 𝑦 = 2 , 𝑥 = 7 and 𝑦 = 1 1 4
  • D 𝑥 = 0 𝑦 = 2 a n d , 𝑥 = 1 . 4 and 𝑦 = 0 . 8 8
  • E 𝑥 = 1 and 𝑦 = 2 , 𝑥 = 1 . 4 and 𝑦 = 0 . 8 8

Q10:

Find all the real solutions to the system of equations 𝑦 = 2 𝑥 + 4 𝑥 + 6 , 𝑦 = 4 𝑥 + 2 2 𝑥 + 2 4 .

  • A 𝑥 = 1 . 3 and 𝑦 = 2 . 5 8 , 𝑥 = 1 1 . 7 and 𝑦 = 6 4 . 2
  • B 𝑥 = 1 and 𝑦 = 6 , 𝑥 = 3 and 𝑦 = 1 2 6
  • C 𝑥 = 1 . 5 and 𝑦 = 4 . 5 , 𝑥 = 4 and 𝑦 = 4 2
  • D 𝑥 = 1 . 1 5 and 𝑦 = 1 . 2 4 5 , 𝑥 = 7 . 8 5 and 𝑦 = 9 7 . 7 9
  • EThere are no solutions.

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