Lesson Worksheet: Introduction to the System of Linear Equations Mathematics • 10th Grade

In this worksheet, we will practice expressing a system of linear equations as a matrix equation.


Express the simultaneous equations 3π‘₯+2𝑦=12,3π‘₯+𝑦=7 as a matrix equation.

  • A3321π‘₯π‘¦οŸ=712
  • B3231π‘₯π‘¦οŸ=712
  • C3213π‘₯π‘¦οŸ=127
  • D3231π‘₯π‘¦οŸ=127
  • E3321π‘₯π‘¦οŸ=127


Express the following set of simultaneous equations as a matrix equation: 7π‘₯βˆ’3𝑦+6𝑧=5,5π‘₯βˆ’2𝑦+2𝑧=11,2π‘₯βˆ’3𝑦+8𝑧=10.

  • A752βˆ’3βˆ’2βˆ’3628π‘₯𝑦𝑧=51110
  • B752βˆ’3βˆ’2βˆ’3628π‘₯𝑦𝑧=10511
  • C7βˆ’365βˆ’22238π‘₯𝑦𝑧=10511
  • D6βˆ’372βˆ’25832π‘₯𝑦𝑧=51110
  • E7βˆ’365βˆ’222βˆ’38π‘₯𝑦𝑧=51110


True or False: The number of columns of a coefficient matrix in a matrix equation represents the number of variables.

  • ATrue
  • BFalse


Write down the set of simultaneous equations that could be solved using the given matrix equation. 3324ο ο“π‘Žπ‘οŸ=1012

  • A3π‘Ž+3𝑏=104π‘Ž+2𝑏=12
  • B3π‘Ž+3𝑏=102π‘Ž+4𝑏=12
  • C3π‘Ž+2𝑏=103π‘Ž+4𝑏=12
  • D3π‘Ž+2𝑏=123π‘Ž+4𝑏=10
  • E3π‘Ž+3𝑏=122π‘Ž+4𝑏=10


Write down the set of simultaneous equations that could be solved using the matrix equation 224βˆ’1βˆ’1βˆ’1256ο€ο˜π‘π‘žπ‘Ÿο€=41410.

  • A2π‘βˆ’π‘ž+2π‘Ÿ=14, 2π‘βˆ’π‘ž+5π‘Ÿ=10, 4π‘βˆ’π‘ž+6π‘Ÿ=4
  • B2𝑝+4π‘ž+2π‘Ÿ=4, βˆ’π‘βˆ’π‘žβˆ’π‘Ÿ=14, 2𝑝+6π‘ž+5π‘Ÿ=10
  • C2π‘βˆ’π‘ž+2π‘Ÿ=4, 2π‘βˆ’π‘ž+5π‘Ÿ=14, 4π‘βˆ’π‘ž+6π‘Ÿ=10
  • D2𝑝+2π‘ž+4π‘Ÿ=14, βˆ’π‘βˆ’π‘žβˆ’π‘Ÿ=10, 2𝑝+5π‘ž+6π‘Ÿ=4
  • E2𝑝+2π‘ž+4π‘Ÿ=4, βˆ’π‘βˆ’π‘žβˆ’π‘Ÿ=14, 2𝑝+5π‘ž+6π‘Ÿ=10


Express the simultaneous equations 3π‘₯βˆ’24=βˆ’8𝑦π‘₯=3βˆ’π‘¦ as a matrix equation.

  • A3βˆ’81βˆ’1π‘₯π‘¦οŸ=243
  • B3181π‘₯π‘¦οŸ=243
  • C3811π‘₯π‘¦οŸ=243
  • D3181π‘₯π‘¦οŸ=324
  • E3811π‘₯π‘¦οŸ=324


Express the set of simultaneous equations 3π‘₯=12+5𝑦+2𝑧,π‘₯βˆ’5𝑦=21,11π‘₯βˆ’8𝑦=βˆ’10+2𝑧 as a matrix equation.

  • A3111βˆ’5βˆ’5βˆ’8βˆ’20βˆ’2π‘₯𝑦𝑧=1221βˆ’10
  • B3βˆ’5βˆ’21βˆ’5011βˆ’8βˆ’2π‘₯𝑦𝑧=21βˆ’1012
  • C3111βˆ’5βˆ’5βˆ’8βˆ’20βˆ’2π‘₯𝑦𝑧=21βˆ’1012
  • D3βˆ’5βˆ’21βˆ’5011βˆ’8βˆ’2π‘₯𝑦𝑧=1221βˆ’10
  • E3521βˆ’5011βˆ’82π‘₯𝑦𝑧=1221βˆ’10


Write down the set of simultaneous equations that could be solved using the given matrix equation. 1βˆ’2βˆ’410134βˆ’8ο€ο˜π‘π‘žπ‘Ÿο€=11610

  • Aπ‘βˆ’2π‘žβˆ’4π‘Ÿ=11𝑝+π‘ž=63𝑝+4π‘žβˆ’8π‘Ÿ=10
  • B𝑝+π‘ž+3π‘Ÿ=11βˆ’2𝑝+4π‘Ÿ=6βˆ’4𝑝+π‘žβˆ’8π‘Ÿ=10
  • Cπ‘βˆ’2π‘žβˆ’4π‘Ÿ=6𝑝+π‘Ÿ=103𝑝+4π‘žβˆ’8π‘Ÿ=11
  • Dπ‘βˆ’2π‘žβˆ’4π‘Ÿ=11𝑝+π‘Ÿ=63𝑝+4π‘žβˆ’8π‘Ÿ=10
  • E𝑝+π‘ž+3π‘Ÿ=6βˆ’2𝑝+4π‘Ÿ=10βˆ’4𝑝+π‘žβˆ’8π‘Ÿ=11


Find the matrix 𝐴 such that 𝐴⎑⎒⎒⎣π‘₯π‘₯π‘₯π‘₯⎀βŽ₯βŽ₯⎦=⎑⎒⎒⎒⎣π‘₯+3π‘₯+2π‘₯2π‘₯+π‘₯6π‘₯π‘₯+3π‘₯+π‘₯⎀βŽ₯βŽ₯βŽ₯⎦.οŠͺοŠͺ

  • A⎑⎒⎒⎣1101300322600001⎀βŽ₯βŽ₯⎦
  • B⎑⎒⎒⎣1261310320010000⎀βŽ₯βŽ₯⎦
  • C⎑⎒⎒⎣1320210060001310⎀βŽ₯βŽ₯⎦
  • D⎑⎒⎒⎣1201316320010000⎀βŽ₯βŽ₯⎦
  • E⎑⎒⎒⎣1320102000601301⎀βŽ₯βŽ₯⎦


Consider a system of linear equations written in matrix form as 𝐴𝑋=𝐡. If the order of matrix 𝐴 is π‘šΓ—π‘› and the order of matrix 𝑋 is 𝑛×1, how many equations does the system have?

  • A𝑛
  • Bπ‘š
  • Cπ‘šΓ—π‘›
  • D1

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