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Exercises for Question Type 2: Finding a unique solution to a system of equations algebraically using matrices or Gaussian elimination - IB | RevisionDojo

Question 1

Solve the following system of equations:

\begin{cases} 7x - 5y = 1 \\ 3x + 2y = 17 \end{cases}

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Question 2

Solve the triangular system using Gaussian elimination:

\begin{cases} x + 2y - z = 1 \\ y + 3z = 7 \\ 2z = 8 \end{cases}

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Question 3

Solve the system using elimination or an augmented matrix:

\begin{cases} 4x - y = 9 \\ 2x + 3y = 13 \end{cases}

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Question 4

Solve the system by Gaussian elimination:

\begin{cases} x + y + z = 6 \\ 2x - y + z = 3 \\ - x + 2y + z = 7 \end{cases}

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Question 5

Solve the system using Gaussian elimination:

\begin{cases} 2x + 3y = 7 \\ 4x - y = 5 \end{cases}

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Question 6

Use Gaussian elimination to solve the system and justify uniqueness by noting a nonzero pivot in each column:

\begin{cases} 2x + y = 5 \\ x + 3y + z = 10 \\ y + 2z = 8 \end{cases}

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Question 7

Solve the system using row-reduction (Gaussian elimination):

\begin{cases} 2x + y = 5 \\ y + 3z = 10 \\ x - z = 1 \end{cases}

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Question 8

Use Gaussian elimination to solve:

\begin{cases} 3x - y + 2z = 12 \\ 2x + y - z = 3 \\ x + 2y + z = 9 \end{cases}

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Question 9

Solve the system using Gaussian elimination:

\begin{cases} 1.5x - 0.5y = 2 \\ 0.2x + 0.8y = 1 \end{cases}

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Question 10

Solve the system using Gaussian elimination:

\begin{cases} 0x + 2y + z = 4 \\ x + y + z = 6 \\ 2x - y + 3z = 5 \end{cases}

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Question Type 2: Finding a unique solution to a system of equations algebraically using matrices or Gaussian elimination Exercises