Worksheet: Solving Systems of Nonlinear Equations Graphically

In this worksheet, we will practice graphing a system of equations, one of which is linear and the other nonlinear, to find their solution.


Use the graph shown to find the value or values of 𝑥 that are the solution of the system of equations 𝑦=32𝑥,𝑦=𝑥.

  • A𝑥=1 and 𝑥=9
  • B𝑥=0
  • C𝑥=4
  • D𝑥=2 and 𝑥=2
  • E𝑥=3 and 𝑥=1


Using the given graph, determine the solution to the simultaneous equations 𝑦=2𝑥+1,𝑦=𝑥+1.

  • A𝑥=1, 𝑦=0 and 𝑥=5, 𝑦=2
  • B𝑥=0, 𝑦=1 and 𝑥=2, 𝑦=5
  • C𝑥=0, 𝑦=1 and 𝑥=2, 𝑦=5
  • D𝑥=0, 𝑦=1 and 𝑥=2, 𝑦=5
  • E𝑥=1, 𝑦=0 and 𝑥=5, 𝑦=2


What graph can be used to solve the set of simultaneous equations 𝑦=𝑥2+2,𝑦=𝑥𝑥5?

  • A
  • B
  • C
  • D
  • E


Which of the following sets of simultaneous equations could be solved using the given graph?

  • A𝑦=𝑥2+3,𝑦=𝑥1
  • B𝑦=𝑥3+2,𝑦=𝑥1
  • C𝑦=𝑥32,𝑦=𝑥1
  • D𝑦=𝑥32,𝑦=𝑥+1
  • E𝑦=𝑥23,𝑦=𝑥+1


Using the graph, determine which of the following points is an estimate for the solution to the simultaneous equations 𝑦=𝑥2+1,𝑦=𝑥+3𝑥+2.

  • A(3.4,2.6), (0.3,1.2)
  • B(3.2,1.2), (0.3,1.2)
  • C(3.2,2.6), (0.1,1.2)
  • D(3.2,2.8), (0.3,1.4)
  • E(3.2,2.6), (0.3,1.2)

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