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

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


Given that 581βˆ’8π‘₯π‘¦οŸ=ο”βˆ’431, determine the values of π‘₯ and 𝑦.

  • Aπ‘₯=βˆ’43, 𝑦=1
  • Bπ‘₯=13, 𝑦=βˆ’7
  • Cπ‘₯=βˆ’1, 𝑦=βˆ’7
  • Dπ‘₯=βˆ’7, 𝑦=βˆ’1


Given that 𝐴=2βˆ’5βˆ’8βˆ’9,𝐴π‘₯π‘¦οŸ=ο”βˆ’28, what is the value of 𝑦?


Consider the simultaneous equations 4π‘₯βˆ’2𝑦=0,3𝑦+5π‘₯=βˆ’11.

Express the given simultaneous equations as a matrix equation.

  • A4βˆ’253π‘₯π‘¦οŸ=ο”βˆ’110
  • B4βˆ’235π‘₯π‘¦οŸ=0βˆ’11
  • C4βˆ’253π‘₯π‘¦οŸ=0βˆ’11
  • D4βˆ’235π‘₯π‘¦οŸ=ο”βˆ’110
  • E43βˆ’25π‘₯π‘¦οŸ=0βˆ’11

Write down the inverse of the coefficient matrix.

  • A11452βˆ’34
  • B12232βˆ’54
  • C12652βˆ’34
  • D1232βˆ’54
  • E12632βˆ’54

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

  • Aπ‘₯π‘¦οŸ=1βˆ’1
  • Bπ‘₯π‘¦οŸ=21
  • Cπ‘₯π‘¦οŸ=12
  • Dπ‘₯π‘¦οŸ=ο”βˆ’1βˆ’2
  • Eπ‘₯π‘¦οŸ=ο”βˆ’1βˆ’3


Use matrices to solve the system βˆ’π‘₯+5𝑦=8,βˆ’3π‘₯+𝑦=8.

  • Aπ‘₯=167, 𝑦=βˆ’87
  • Bπ‘₯=5, 𝑦=135
  • Cπ‘₯=βˆ’167, 𝑦=87
  • Dπ‘₯=2, 𝑦=βˆ’1
  • Eπ‘₯=87, 𝑦=βˆ’167


Given that ο”βˆ’11βˆ’1βˆ’1π‘₯π‘¦οŸ=ο”βˆ’75, find π‘₯π‘¦οŸ.

  • Aο”βˆ’61
  • Bο”βˆ’73
  • C3βˆ’7
  • D1βˆ’6


Use matrices to solve the system of equations 3π‘₯βˆ’24=βˆ’8𝑦,π‘₯=3βˆ’π‘¦.

  • Aπ‘₯π‘¦οŸ=30
  • Bπ‘₯π‘¦οŸ=ο”βˆ’36
  • Cπ‘₯π‘¦οŸ=4βˆ’1
  • Dπ‘₯π‘¦οŸ=6βˆ’3
  • Eπ‘₯π‘¦οŸ=03


Use matrices to solve the system of equations 𝑛+1=2π‘š,𝑛=π‘š+2.

  • Aο“π‘šπ‘›οŸ=24
  • Bο“π‘šπ‘›οŸ=13
  • Cο“π‘šπ‘›οŸ=ο”βˆ’11
  • Dο“π‘šπ‘›οŸ=ο”βˆ’20
  • Eο“π‘šπ‘›οŸ=35


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.


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.


The straight line whose equation is 𝑦+π‘Žπ‘₯=𝑐 passes through the two points (βˆ’5,5) and (3,10). Using matrices, find π‘Ž and 𝑐.

  • Aπ‘Ž=βˆ’58, 𝑐=658
  • Bπ‘Ž=βˆ’158, 𝑐=358
  • Cπ‘Ž=3, 𝑐=19
  • Dπ‘Ž=10, 𝑐=βˆ’45
  • Eπ‘Ž=5, 𝑐=βˆ’65

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

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