Lesson Worksheet: Solving Systems of Quadratic Equations Mathematics

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

Q1:

Find all the real solutions to the following system of equations 𝑦=−2𝑥+12𝑥−13,𝑦=−𝑥3+2𝑥+2.

  • A𝑥=−3 and 𝑦=−67
  • BThere are no solutions.
  • C𝑥=9 and 𝑦=−67
  • D𝑥=3 and 𝑦=5
  • E𝑥=6 and 𝑦=−13

Q2:

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

  • A𝑥=2 or 𝑥=−2, 𝑦=1 or 𝑦=5
  • B𝑥=4 or 𝑥=−4, 𝑦=3 or 𝑦=11
  • CThere are no solutions.
  • D𝑥=4 and 𝑦=11
  • E𝑥=16 and 𝑦=−7

Q3:

Find all the real solutions to the system of equations: 4𝑦+𝑥−4𝑥−40=0,2𝑦−72𝑥−6𝑥+4=0.

  • A𝑥=−2.5 and 𝑦=5.9375, 𝑥=2.2 and 𝑦=11.29
  • B𝑥=−3 and 𝑦=4.75, 𝑥=2 and 𝑦=11
  • C𝑥=−2.5 and 𝑦=−5.9375, 𝑥=2.2 and 𝑦=−10.99
  • D𝑥=−2 and 𝑦=7, 𝑥=3 and 𝑦=10.75
  • EThere are no solutions.

Q4:

Find all the real solutions to the system of equations 5𝑦−𝑥+9𝑥−24=0,3𝑦+𝑥−9𝑥+18=0.

  • A𝑥=4.5 and 𝑦=−3
  • B𝑥=4.5 and 𝑦=0.75
  • CThere are no solutions.
  • D𝑥=8.7 and 𝑦=−5.25
  • E𝑥=12.6 and 𝑦=−21

Q5:

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

  • A𝑥=1 and 𝑦=0, 𝑥=−2 and 𝑦=6
  • BThere are no solutions.
  • C𝑥=1 and 𝑦=0, 𝑥=2 and 𝑦=−6
  • D𝑥=−1 and 𝑦=0, 𝑥=2 and 𝑦=−6
  • E𝑥=−1 and 𝑦=0, 𝑥=103 and 𝑦=−269

Q6:

Find all the real solutions to the system of equations 𝑦=𝑥−7,𝑦=(𝑥+1)(𝑥−5).

  • A𝑥=−3 and 𝑦=2
  • B𝑥=−0.5 and 𝑦=−6.75
  • C𝑥=0.5 and 𝑦=−6.75
  • D𝑥=3 and 𝑦=2
  • E𝑥=−2 and 𝑦=−3

Q7:

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

  • AThere are no solutions.
  • B𝑥=0 and 𝑦=2, 𝑥=−7 and 𝑦=114
  • C𝑥=0 and 𝑦=2, 𝑥=−0.6 and 𝑦=0.08
  • D𝑥=1 and 𝑦=−2, 𝑥=−1.4 and 𝑦=0.88
  • E𝑥=0 and 𝑦=2, 𝑥=−1.4 and 𝑦=0.88

Q8:

Find all the real solutions to the system of equations 𝑦=−2𝑥+4𝑥+6,𝑦=4𝑥+22𝑥+24.

  • A𝑥=−1.15 and 𝑦=−1.245, 𝑥=−7.85 and 𝑦=97.79
  • B𝑥=−1.5 and 𝑦=−4.5, 𝑥=−4 and 𝑦=−42
  • C𝑥=−1.3 and 𝑦=−2.58, 𝑥=−11.7 and 𝑦=−64.2
  • DThere are no solutions.
  • E𝑥=−1 and 𝑦=6, 𝑥=3 and 𝑦=126

Q9:

Use the graph to solve the system of equations

𝑦=3𝑥+36𝑥+96,𝑦=−5𝑥+10𝑥+40.

  • A𝑥=0 and 𝑦=40,𝑥=−7.5 and 𝑦=−10
  • B𝑥=0 and 𝑦=40
  • CThere are no solutions.
  • D𝑥=−4 and 𝑦=0,𝑥=−8 and 𝑦=0
  • E𝑥=−7.5 and 𝑦=−10

Q10:

Use the graph to solve the system of equations 𝑦=𝑥−10𝑥+32,𝑦=−2𝑥+20𝑥−43.

  • A𝑥=7 and 𝑦=5
  • B𝑥=6 and 𝑦=10
  • C𝑥=4 and 𝑦=5
  • D𝑥=10 and 𝑦=6
  • E𝑥=5 and 𝑦=7

This lesson includes 2 additional questions for subscribers.

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