Worksheet: Solving Systems of Nonlinear Equations Using Graphing

In this worksheet, we will practice solving a system of two nonlinear equations or a linear equation and a nonlinear equation.

Q1:

Use the shown graph to solve the simultaneous equations

  • A 𝑥 = 3 and 𝑦 = 2 , 𝑥 = 3 and 𝑦 = 1
  • B 𝑥 = 2 and 𝑦 = 0 , 𝑥 = 1 and 𝑦 = 3
  • C 𝑥 = 0 and 𝑦 = 2 , 𝑥 = 3 and 𝑦 = 1
  • D 𝑥 = 2 and 𝑦 = 3 , 𝑥 = 1 and 𝑦 = 0
  • E 𝑥 = 4 and 𝑦 = 5 , 𝑥 = 1 and 𝑦 = 0

Q2:

Use the shown graph to solve the simultaneous equations

  • A 𝑥 = 0 and 𝑦 = 5 , 𝑥 = 2 and 𝑦 = 7
  • B 𝑥 = 2 and 𝑦 = 3 , 𝑥 = 6 and 𝑦 = 1 1
  • C 𝑥 = 2 and 𝑦 = 7 , 𝑥 = 3 and 𝑦 = 8
  • D 𝑥 = 2 and 𝑦 = 3 , 𝑥 = 2 and 𝑦 = 7
  • E 𝑥 = 0 and 𝑦 = 5 , 𝑥 = 6 and 𝑦 = 1 1

Q3:

Use the shown graph to solve the given simultaneous equations.

  • A 𝑥 = 3 and 𝑦 = 1 , 𝑥 = 1 and 𝑦 = 3
  • B 𝑥 = 0 and 𝑦 = 1 , 𝑥 = 4 and 𝑦 = 4
  • C 𝑥 = 1 and 𝑦 = 0 , 𝑥 = 4 and 𝑦 = 4
  • D 𝑥 = 1 and 𝑦 = 3 , 𝑥 = 3 and 𝑦 = 1
  • E 𝑥 = 1 and 𝑦 = 5 , 𝑥 = 5 and 𝑦 = 1

Q4:

Use the graph to solve the following simultaneous equations:

  • A 𝑥 = 2 and 𝑦 = 3 , 𝑥 = 1 . 5 and 𝑦 = 6 . 5
  • B 𝑥 = 7 and 𝑦 = 2 , 𝑥 = 1 and 𝑦 = 6
  • C 𝑥 = 1 and 𝑦 = 4 , 𝑥 = 3 and 𝑦 = 8
  • D 𝑥 = 3 and 𝑦 = 2 , 𝑥 = 1 and 𝑦 = 6
  • E 𝑥 = 1 and 𝑦 = 4 , 𝑥 = 7 and 𝑦 = 1 2

Q5:

Given that the simultaneous equations are graphically represented in the figure, solve the two equations and find the most accurate estimations of 𝑥 - and 𝑦 -values.

  • A 𝑥 = 2 and 𝑦 = 1 6 , 𝑥 = 1 4 and 𝑦 = 1 1
  • B 𝑥 = 1 6 and 𝑦 = 2 , 𝑥 = 1 1 and 𝑦 = 1 4
  • C 𝑥 = 6 and 𝑦 = 7 , 𝑥 = 1 0 and 𝑦 = 2
  • D 𝑥 = 7 and 𝑦 = 6 , 𝑥 = 2 and 𝑦 = 1 0
  • E 𝑥 = 2 and 𝑦 = 7 , 𝑥 = 0 and 𝑦 = 9

Q6:

Use the graph to solve the system of equations

  • A 𝑥 = 0 and 𝑦 = 2 , 𝑥 = 2 5 and 𝑦 = 3
  • BThere are no solutions.
  • C 𝑥 = 2 and 𝑦 = 0 , 𝑥 = 3 and 𝑦 = 2 5
  • D 𝑥 = 2 and 𝑦 = 0 , 𝑥 = 3 and 𝑦 = 2 5
  • E 𝑥 = 0 and 𝑦 = 2 , 𝑥 = 2 5 and 𝑦 = 3

Q7:

Use the graph to solve the system of equations

  • A 𝑥 = 4 and 𝑦 = 0 , 𝑥 = 8 and 𝑦 = 0
  • B 𝑥 = 0 and 𝑦 = 4 0 , 𝑥 = 7 . 5 and 𝑦 = 1 0
  • C 𝑥 = 0 and 𝑦 = 4 0
  • DThere are no solutions.
  • E 𝑥 = 7 . 5 and 𝑦 = 1 0

Q8:

Use the graph to solve the system of equations

  • A 𝑥 = 6 and 𝑦 = 1 0
  • B 𝑥 = 7 and 𝑦 = 5
  • C 𝑥 = 1 0 and 𝑦 = 6
  • D 𝑥 = 5 and 𝑦 = 7
  • E 𝑥 = 4 and 𝑦 = 5

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