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Exercises for Question Type 1: Finding a unique solution to a system of equations algebraically using elimination or substitution - IB | RevisionDojo

Question 1

Solve the system algebraically for $x$ , $y$ , and $z$ :

\begin{cases} 2x + y - z = 3 \\ x + 3y + 2z = 14 \\ 3x - y + z = 4 \end{cases}

[5]

Question 2

Solve the system algebraically for $x$ and $y$ :

\begin{cases} 3x + 4y = -2 \\ 5x - 2y = 14 \end{cases}

[5]

Question 3

Solve the system algebraically for $x$ , $y$ , and $z$ :

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

[5]

Question 4

Solve the system algebraically for $x$ and $y$ :

\begin{cases} 2x + 3y = 13 \\ 5x - 3y = 7 \end{cases}

[4]

Question 5

Solve the system algebraically for $x$ and $y$ :

\begin{cases} 2x + y = 7 \\ 3x + y = 10 \end{cases}

[3]

Question 6

Solve the system algebraically for $x$ , $y$ , and $z$ :

\begin{cases} 4x - y + 2z = 1 \\ -2x + 3y + z = 9 \\ x + y - 3z = -8 \end{cases}

[6]

Question 7

Solve the system algebraically for $x$ and $y$ :

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

[3]

Question 8

Solve the system algebraically for $x$ , $y$ , and $z$ :

\begin{cases} 0.5x + y - 0.5z = 1 \\ 1.5x - y + 0.5z = 2 \\ x + 2y + z = 7 \end{cases}

[5]

Question 9

Adult tickets cost $12 and child tickets cost $8. If $120$ tickets were sold for a total of $1200, solve for the numbers of adult tickets $x$ and child tickets $y$ using the system:

\begin{cases} x + y = 120 \\ 12x + 8y = 1200 \end{cases}

[4]

Question 10

Solve the system algebraically for $x$ and $y$ :

\begin{cases} 0.4x + 0.2y = 3 \\ 1.2x - 0.1y = 5 \end{cases}

[5]

Question 11

Solve the system algebraically for $x$ and $y$ :

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

[4]

Question 12

Solve the system algebraically for $x$ and $y$ :

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

[5]

Question 13

Solve the system algebraically for $x$ and $y$ :

\begin{cases} x + y = 7 \\ x - y = 1 \end{cases}

[3]

Question Type 1: Finding a unique solution to a system of equations algebraically using elimination or substitution Exercises