Lesson Worksheet: Linear–Quadratic Systems of Equations Mathematics

In this worksheet, we will practice solving linear–quadratic systems of equations.

Q1:

Find all of the solutions to the simultaneous equations 𝑦+𝑥=7 and 2𝑥+𝑥+3𝑦=21.

  • A𝑥=1, 𝑦=5; 𝑥=0, 𝑦=7
  • B𝑥=1, 𝑦=5; 𝑥=0, 𝑦=6
  • C𝑥=1, 𝑦=6; 𝑥=0, 𝑦=7
  • D𝑥=2, 𝑦=6; 𝑥=1, 𝑦=7

Q2:

Find the set of points of intersection of the graphs of 𝑥+5𝑦=0 and 𝑦=𝑥.

  • A{(0,0),(5,25)}
  • B{(0,0),(5,25)}
  • C{(0,0),(25,5)}
  • D{(0,0),(25,5)}

Q3:

Given that 𝑥+𝑥𝑦=18, and 𝑥+𝑦=6, find the value of 𝑥.

Q4:

Find the set of points of intersection of the graphs of 𝑥+𝑦=8 and 𝑥+𝑦=50.

  • A{(7,1),(1,7)}
  • B{(15,7),(9,1)}
  • C{(7,15),(1,9)}
  • D{(7,7),(1,1)}

Q5:

Find all of the solutions to the simultaneous equations 𝑦+2𝑥=3 and 𝑥+𝑥𝑦+𝑦=3.

  • A𝑥=2𝑦=5𝑥=1𝑦=1,;,
  • B𝑥=2𝑦=1𝑥=1𝑦=1,;,
  • C𝑥=4𝑦=1𝑥=1𝑦=1,;,
  • D𝑥=2𝑦=5𝑥=1𝑦=1,;,

Q6:

Find all of the solutions to the simultaneous equations 𝑥𝑦=26 and 𝑥𝑦=120.

  • A𝑥=30𝑦=4𝑥=4𝑦=30,;,
  • B𝑥=4𝑦=60𝑥=30𝑦=3,;,
  • C𝑥=4𝑦=30𝑥=30𝑦=4,;,
  • D𝑥=20𝑦=6𝑥=6𝑦=20,;,
  • E𝑥=86𝑦=60𝑥=18𝑦=8,;,

Q7:

Solve the simultaneous equations 𝑦=𝑥4,𝑥5+𝑦3=4, giving your answers to two decimal places.

  • A𝑥=4.46 and 𝑦=0.46, 𝑥=2.46 and 𝑦=1.54
  • B𝑥=0.56 and 𝑦=3.44, 𝑥=4.44 and 𝑦=0.44
  • C𝑥=0.44 and 𝑦=4.44, 𝑥=3.44 and 𝑦=0.56
  • D𝑥=6.47 and 𝑦=2.47, 𝑥=1.47 and 𝑦=5.47
  • E𝑥=3.10 and 𝑦=7.10, 𝑥=7.10 and 𝑦=3.10

Q8:

Find all of the solutions to the simultaneous equations 𝑥𝑦=6 and 𝑥9𝑥𝑦+𝑦=36.

  • A𝑥=12, 𝑦=0; 𝑥=13, 𝑦=6
  • B𝑥=6, 𝑦=63; 𝑥=0, 𝑦=87
  • C𝑥=0, 𝑦=6; 𝑥=6, 𝑦=0
  • D𝑥=6, 𝑦=63; 𝑥=0, 𝑦=9

Q9:

Find the set of points of intersection of the graphs of 𝑥𝑦=0 and 6𝑥𝑦=45.

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

Q10:

Find the set of points of intersection of the graphs of 𝑥=6+𝑦 and 𝑥𝑦=24.

  • A{(7,1)}
  • B{(1,7)}
  • C{(5,1)}
  • D{(1,5)}

This lesson includes 56 additional questions and 509 additional question variations for subscribers.

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