Lesson Worksheet: Solving Systems of Quadratic Equations Mathematics

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

Question 1

Find all the real solutions to the following system of equations 𝑦=2𝑥+12𝑥13,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

Question 2

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

Question 3

Find all the real solutions to the system of equations: 4𝑦+𝑥4𝑥40=0,2𝑦72𝑥6𝑥+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.

Question 4

Find all the real solutions to the system of equations 5𝑦𝑥+9𝑥24=0,3𝑦+𝑥9𝑥+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

Question 5

Find all the real solutions to the system of equations 𝑦=𝑥3𝑥4,𝑦=2𝑥4𝑥6.

  • 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

Question 6

Find all the real solutions to the system of equations 𝑦=𝑥7,𝑦=(𝑥+1)(𝑥5).

  • 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

Question 7

Find all the real solutions to the system of equations 𝑦=3𝑥+5𝑥+2,𝑦=2𝑥2𝑥+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

Question 8

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

Question 9

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

Question 10

Use the graph to solve the system of equations 𝑦=𝑥10𝑥+32,𝑦=2𝑥+20𝑥43.

  • 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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