Worksheet: Nonlinear System of Equations

In this worksheet, we will practice finding values that satisfy two exponential equations in two variables simultaneously.

Q1:

Find the solution set of 3 × 3 = 2 7 and 3 + 3 = 1 2 .

  • A { ( 2 , 2 ) , ( 2 , 2 ) }
  • B { ( 3 , 9 ) , ( 9 , 3 ) }
  • C { ( 3 , 3 ) , ( 3 , 3 ) }
  • D { ( 1 , 2 ) , ( 2 , 1 ) }
  • E { ( 1 , 1 ) , ( 1 , 1 ) }

Q2:

Given that 2 × 4 = 2 , 0 4 8 and 2 × 4 = 1 , 0 2 4 , determine the values of 𝑚 and 𝑛 .

  • A 𝑚 = 2 , 𝑛 = 4
  • B 𝑚 = 3 , 𝑛 = 4
  • C 𝑚 = 2 , 𝑛 = 4
  • D 𝑚 = 3 , 𝑛 = 4

Q3:

Given that 𝑓 ( 𝑥 ) = 2 , determine the value of 𝑥 that satisfies the equation 𝑓 ( 𝑥 + 5 ) + 𝑓 ( 𝑥 5 ) = 1 , 0 2 5 .

  • A 2
  • B 32
  • C 25
  • D 5
  • E 10

Q4:

Use the graph to solve the following system of equations:

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

Q5:

Use the graph to solve the following system of equations:

  • A 𝑥 = 1 and 𝑦 = 5
  • B 𝑥 = 5 and 𝑦 = 2
  • C 𝑥 = 5 and 𝑦 = 1
  • D 𝑥 = 2 and 𝑦 = 5
  • E 𝑥 = 5 and 𝑦 = 2 . 5

Q6:

Find the solution set of 8 × 8 = 5 1 2 and 8 + 8 = 7 2 .

  • A { ( 7 , 7 ) , ( 7 , 7 ) }
  • B { ( 8 , 6 4 ) , ( 6 4 , 8 ) }
  • C { ( 2 8 , 2 8 ) , ( 2 8 , 2 8 ) }
  • D { ( 1 , 2 ) , ( 2 , 1 ) }
  • E { ( 1 , 1 ) , ( 1 , 1 ) }

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