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Lesson Worksheet: Solving a System of Two Equations Using a Matrix Inverse Mathematics • 10th Grade

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In this worksheet, we will practice solving a system of two linear equations using the inverse of the matrix of coefficients.

Q1:

Given that 581−8𝑥𝑦=−431, determine the values of 𝑥 and 𝑦.

  • A𝑥=−43, 𝑦=1
  • B𝑥=13, 𝑦=−7
  • C𝑥=−1, 𝑦=−7
  • D𝑥=−7, 𝑦=−1

Q2:

Given that 𝐴=2−5−8−9,𝐴𝑥𝑦=−28, what is the value of 𝑦?

Q3:

Consider the simultaneous equations 4𝑥−2𝑦=0,3𝑦+5𝑥=−11.

Express the given simultaneous equations as a matrix equation.

  • A4−253𝑥𝑦=−110
  • B4−235𝑥𝑦=0−11
  • C4−253𝑥𝑦=0−11
  • D4−235𝑥𝑦=−110
  • E43−25𝑥𝑦=0−11

Write down the inverse of the coefficient matrix.

  • A11452−34
  • B12232−54
  • C12652−34
  • D1232−54
  • E12632−54

Multiply through by the inverse, on the left-hand side, to solve the matrix equation.

  • A𝑥𝑦=1−1
  • B𝑥𝑦=21
  • C𝑥𝑦=12
  • D𝑥𝑦=−1−2
  • E𝑥𝑦=−1−3

Q4:

Use matrices to solve the system −𝑥+5𝑦=8,−3𝑥+𝑦=8.

  • A𝑥=167, 𝑦=−87
  • B𝑥=5, 𝑦=135
  • C𝑥=−167, 𝑦=87
  • D𝑥=2, 𝑦=−1
  • E𝑥=87, 𝑦=−167

Q5:

Given that −11−1−1𝑥𝑦=−75, find 𝑥𝑦.

  • A−61
  • B−73
  • C3−7
  • D1−6

Q6:

Use matrices to solve the system of equations 3𝑥−24=−8𝑦,𝑥=3−𝑦.

  • A𝑥𝑦=30
  • B𝑥𝑦=−36
  • C𝑥𝑦=4−1
  • D𝑥𝑦=6−3
  • E𝑥𝑦=03

Q7:

Use matrices to solve the system of equations 𝑛+1=2𝑚,𝑛=𝑚+2.

  • A𝑚𝑛=24
  • B𝑚𝑛=13
  • C𝑚𝑛=−11
  • D𝑚𝑛=−20
  • E𝑚𝑛=35

Q8:

The length of a rectangle is 6 cm more than twice its width, and twice its length is 39 cm more than its width. Given this, use matrices to determine the perimeter of the rectangle.

Q9:

A girl bought 6 kilograms of flour and 5 kilograms of butter for 503 LE, and her friend bought 4 kg of flour and 7 kg of butter for 669 LE. Using matrices, find the price per kilogram of both flour and butter.

  • AA kilogram of flour costs 6 LE and a kilogram of butter costs 110 LE.
  • BA kilogram of flour costs 91 LE and a kilogram of butter costs 8 LE.
  • CA kilogram of flour costs 61 LE and a kilogram of butter costs 46 LE.
  • DA kilogram of flour costs 8 LE and a kilogram of butter costs 91 LE.

Q10:

The straight line whose equation is 𝑦+𝑎𝑥=𝑐 passes through the two points (−5,5) and (3,10). Using matrices, find 𝑎 and 𝑐.

  • A𝑎=−58, 𝑐=658
  • B𝑎=−158, 𝑐=358
  • C𝑎=3, 𝑐=19
  • D𝑎=10, 𝑐=−45
  • E𝑎=5, 𝑐=−65

This lesson includes 30 additional questions and 178 additional question variations for subscribers.

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