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AHL 1.16—Solution of systems of linear equations - IB Questionbank | RevisionDojo

Practice AHL 1.16—Solution of systems of linear equations with authentic IB Mathematics Analysis and Approaches (AA) exam questions for both SL and HL students. This question bank mirrors Paper 1, 2, 3 structure, covering key topics like functions and equations, calculus, complex numbers, sequences and series, and probability and statistics. Get instant solutions, detailed explanations, and build exam confidence with questions in the style of IB examiners.

Paper

Level

Question 1

HLPaper 1

Solve the following simultaneous equations:

$2x + y = 7 \\ 3x - y = 3$

[5]

Question 2

HLPaper 1

Solve the following simultaneous equations:

$2x + 3y - z = 15 \\ x - 2y + 4z = 80 \\ 3x + y + 2z = 75$

[6]

Question 3

HLPaper 1

Solve the following simultaneous equations:

$x + y + z = 6 \\ 2x - y + 3z = 9 \\ x + 2y - z = 2$

[6]

Question 4

HLPaper 1

Given that P = $\begin{pmatrix} 3 & 2 \\ -1 & 4 \end{pmatrix}$ and Q = $\begin{pmatrix} 1 & -3 \\ 5 & 0 \end{pmatrix}$ . Find

P + 3Q

[3]

Question 5

HLPaper 1

The line $y = x+1$ intersects the curve $x^2 + y = 7$ at points $A$ and $B$ .

Calculate the coordinates of $A$ and of $B$ .

[6]

Question 6

HLPaper 1

Solve the pair of simultaneous equations:

$x + y = 7 \\ x^2 + y^2 = 25$

[4]

Question 7

HLPaper 1

Solve the pair of simultaneous equations:

$x^2 + y = 7 \\ y = x + 1$

[6]

Question 8

HLPaper 1

Solve the pair of simultaneous equations:

$x - y = 1$

$\frac{4}{x} - \frac{1}{y} = 1$

[5]

Question 9

HLPaper 1

Given the matrices $\mathbf{P} = \begin{pmatrix} 4 & -1 \\ 2 & 3 \end{pmatrix}$ , $\mathbf{Q} = \begin{pmatrix} 1 & 5 \\ 0 & -2 \end{pmatrix}$ and $\mathbf{R} = \begin{pmatrix} 3 \\ -1 \end{pmatrix}$ .

Calculate $3\mathbf{P} + \mathbf{Q}$ .

[3]

Question 10

HLPaper 1

Consider two lines in three-dimensional space, given by their vector equations $L_1:\mathbf{r}_1 = \begin{pmatrix} 1 \\ 2 \\ 3 \end{pmatrix} + t \begin{pmatrix} 4 \\ 5 \\ 6 \end{pmatrix}$ and $L_2:\mathbf{r}_2 = \begin{pmatrix} 7 \\ 8 \\ 9 \end{pmatrix} + s \begin{pmatrix} a \\ 1 \\ 2 \end{pmatrix}$ .

Find the value of $a$ for which the lines are skew.

[7]

AHL 1.16—Solution of systems of linear equations Questionbank