IB · Mathematics: Analysis & Approaches SL & HL · Number & algebra

Systems of linear equations: IB Mathematics: Analysis & Approaches questions with answers

Free Systems of linear equations questions for IB Mathematics: Analysis & Approaches (SL & HL), HL only, part of Number & algebra. Each question has the answer and the marking points an examiner would look for.

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Systems of linear equations practice questions

Question 1Structured · 5 marks

Consider the system of equations
x − y + 2z = 4
−2x + y − 2z = −1
−5x + 3y + kz = c
where k, c ∈ ℝ.

(a)

Find the value of k for which the system does not have a unique solution.

[3]
(b)

For this value of k, find the value of c for which the system has infinitely many solutions.

[2]
Show answers and mark scheme
PartAnswer and marking pointsMarks
(a)k = −6
attempt to eliminate a variable, or set the determinant equal to 0 M1
row 3 = −1×row 1 + 2×row 2 for x and y (A1)
k = −6 A1
3
(b)c = −6
c = −(4) + 2(−1) (M1)
c = −6 A1
2
Question 2Structured · 5 marks

Consider the system of equations
x − 3y = −3
−3x + y − 3z = −2
−5x + 7y + kz = c
where k, c ∈ ℝ.

(a)

Find the value of k for which the system does not have a unique solution.

[3]
(b)

For this value of k, find the value of c for which the system has infinitely many solutions.

[2]
Show answers and mark scheme
PartAnswer and marking pointsMarks
(a)k = −3
attempt to eliminate a variable, or set the determinant equal to 0 M1
row 3 = −2×row 1 + 1×row 2 for x and y (A1)
k = −3 A1
3
(b)c = 4
c = −2(−3) + 1(−2) (M1)
c = 4 A1
2
Question 3Structured · 5 marks

Consider the system of equations
x + 3z = −2
−3x + y = 1
−4x + y + kz = c
where k, c ∈ ℝ.

(a)

Find the value of k for which the system does not have a unique solution.

[3]
(b)

For this value of k, find the value of c for which the system has infinitely many solutions.

[2]
Show answers and mark scheme
PartAnswer and marking pointsMarks
(a)k = −3
attempt to eliminate a variable, or set the determinant equal to 0 M1
row 3 = −1×row 1 + 1×row 2 for x and y (A1)
k = −3 A1
3
(b)c = 3
c = −1(−2) + (1) (M1)
c = 3 A1
2
Question 4Structured · 5 marks

Consider the system of equations
x + 3y + 3z = −3
y − z = 0
−2x − 8y + kz = c
where k, c ∈ ℝ.

(a)

Find the value of k for which the system does not have a unique solution.

[3]
(b)

For this value of k, find the value of c for which the system has infinitely many solutions.

[2]
Show answers and mark scheme
PartAnswer and marking pointsMarks
(a)k = −4
attempt to eliminate a variable, or set the determinant equal to 0 M1
row 3 = −2×row 1 − 2×row 2 for x and y (A1)
k = −4 A1
3
(b)c = 6
c = −2(−3) − 2(0) (M1)
c = 6 A1
2

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Original IB-style practice questions written for mentorriyaz.in. These are not IB past paper questions, and this site is not affiliated with or endorsed by the International Baccalaureate Organization. Updated 2026-11-04. Paper generator · mentorriyaz.in