TopicGeneral Maths
Algebra · SS1–SS2
Linear & simultaneous equations
Solving equations with one unknown, and pairs of equations with two unknowns.
Learn
- 1Solving linear equationsAn equation is a balance: do the same to both sides until the letter is alone, and clear fractions by multiplying every term.Done15 min
- 2Simultaneous equationsTwo equations, two unknowns: what the answer means on a graph, and how elimination and substitution find it.Done15 min
- 3Turning words into equationsThe step most marks are lost on: choosing letters, translating each sentence into an equation, and answering the question that was actually asked.Done15 min
Practise
Answer linear & simultaneous equations questions one at a time. You'll know straight away whether you're right, with hints and the working step by step.
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Past questions (118)
From 1983–2025: 76 WAEC, 8 NECO, 34 JAMB. Theory questions first, then objective, newest first.
Theory (60)
- NECO 2024 · Paper 2 · Q1Solve the pair of equations and . Hence, find the positive value of given that .
- NECO 2024 · Paper 2 · Q7Solve the equation .
- WAEC 2024 · Paper 2 · Q2A car travelled a distance of at and at . If the total time for …
- NECO 2023 · Paper 2 · Q7The sum of the ages of a man and his daughter is 60 years. Six years ago, the man's age was three times that of his daughter. Find their present …
- WAEC 2023 · Paper 2 · Q1A car travels a distance of at an average speed of . It then travels further for at an average …
- WAEC 2023 · Paper 2 · Q2In a football match, the tickets for children and adults were sold at D3.00 and D5.00 respectively. 400 people attended the match and D1,700.00 …
- WAEC 2023 · Paper 2 · Q7The sum of three numbers is 81. The second number is twice the first. Given that the third number is 6 more than the second, find the numbers.
- WAEC 2023 · Paper 2 · Q8A tree is due south of a building. Musa is standing due west of the tree. (i) Illustrate the information on a diagram. …
- NECO 2022 · Paper 2 · Q12The pie chart below shows the sectorial allocation of subjects offered by 720 students in a college.
- NECO 2022 · Paper 2 · Q4Find the inverse of the matrix and use it to solve the equations and …
- WAEC 2022 · Paper 2 · Q1Given that , and are consecutive terms of a Geometric Progression (G.P.) with common ratio , find the values of …
- WAEC 2022 · Paper 2 · Q13Find the sum of the first 87 multiples of 5.
- WAEC 2022 · Paper 2 · Q2Make the subject of the relation .
- WAEC 2022 · Paper 2 · Q9Copy and complete the table for the relation for .
- WAEC 2022 · Paper 2 · Q2The total cost of 2 packed lunches and 3 packed breakfasts is $40.00. The cost of 2 packed lunches is $12.00 less than the cost of a packed …
- WAEC 2022 · Paper 2 · Q6The sum of two numbers is 8 and their product is . Find the numbers.
- WAEC 2021 · Paper 2 · Q1Mr Sarfo borrowed $25,000.00 from AFIAK Financial Services at simple interest per annum for 3 years. If he was able to pay back the loan in 2 years at equal yearly instalments, how much did he pay each year?
- WAEC 2021 · Paper 2 · Q2A man left town at 10:00 a.m. and travelled by car to town at an average speed of . He spent 2 hours for a meeting and …
- WAEC 2021 · Paper 2 · Q7Copy and complete the table of values for the relation for .
- WAEC 2021 · Paper 2 · Q8In , . If its area is and is , find .
- WAEC 2021 · Paper 2 · Q7A three-digit number is such that the sum of the digits is 12 and the last digit is three times the first one. If the middle digit is half …
- WAEC 2021 · Paper 2 · Q2The distance between two ports and is . Two ships travel towards each other, one leaving port at …
- WAEC 2021 · Paper 2 · Q6The sum of two numbers is 91. If one-quarter of one of the numbers added to one-fifth of the other is 21, find the numbers.
- WAEC 2021 · Paper 2 · Q7The marked price for an item with a profit of is ₦60,000.00. If the item was sold at a discount of , calculate, correct to one decimal …
- WAEC 2021 · Paper 2 · Q9A tailor had a piece of cloth in the shape of a trapezium. The perpendicular distance between the two parallel edges was . The …
- WAEC 2020 · Paper 2 · Q7The diagram shows a wooden structure in the form of a cone, mounted on a hemispherical base. The vertical height of the cone is …
- WAEC 2020 · Paper 2 · Q1Two fractions have the same denominator, 8. The sum of the two fractions is . If one of the fractions is added to 5 times the other, …
- WAEC 2020 · Paper 2 · Q2The cost of 3 cutlasses and 2 hoes is GH₵ 85.00. If the cost of 2 cutlasses and 3 hoes is GH₵ 90.00, calculate the total cost of a cutlass and …
- WAEC 2020 · Paper 2 · Q6Alidu negotiated to buy a car at GH₵ 27,200.00 from a second-hand car dealer and intended to sell it at a profit of . A week later, when …
- WAEC 2019 · Paper 2 · Q13In the diagram, and are tangents to the circle with centre . , and …
- WAEC 2019 · Paper 2 · Q2Find the equation of the line which passes through the points and .
- WAEC 2019 · Paper 2 · Q10A twenty-kilogram bag of rice is consumed by boys in 10 days. When four more boys joined them, the same quantity of rice lasted only 8 days. …
- WAEC 2019 · Paper 2 · Q6Fred bought a car for $5,600.00 and later sold it at of the cost price. He spent $1,310.00 out of the amount received and invested the …
- WAEC 2018 · Paper 2 · Q2The graph of passes through the point . Find the values of .
- WAEC 2018 · Paper 2 · Q2Musa is three years older than Manya. Seven years ago, Musa was twice as old as Manya. How old are they now?
- WAEC 2018 · Paper 2 · Q4In the diagram, is an isosceles triangle with , and , …
- WAEC 2017 · Paper 2 · Q1If , without using mathematical tables or a calculator, find the value of .
- WAEC 2017 · Paper 2 · Q2Solve the equation .
- WAEC 2017 · Paper 2 · Q6A manufacturing company requires 3 hours of direct labour to process every ₦87.00 worth of raw materials. If the company uses ₦30,450.00 worth …
- WAEC 2017 · Paper 2 · Q3In the diagram, is a triangle with , , and . …
- WAEC 2016 · Paper 2 · Q2Solve: .
- WAEC 2016 · Paper 2 · Q8In the diagram, , , and . If , find the value of .
- WAEC 2015 · Paper 2 · Q7The table is for the relation .
- WAEC 2015 · Paper 2 · Q9The first term of an Arithmetic Progression (A.P.) is . If the ratio of the 7th term to the 9th term is , find the common difference …
- WAEC 2014 · Paper 2 · Q3Solve the simultaneous equations and .
- WAEC 2014 · Paper 2 · Q6If , find .
- WAEC 2014 · Paper 2 · Q1Factorize completely: .
- WAEC 2014 · Paper 2 · Q6In a class of 52 students, 16 are Science students. If of the boys and of the girls are Science students, how many boys are …
- WAEC 2013 · Paper 2 · Q3The present ages of a father and his son are in the ratio . If the son is 15 years old now, in how many years will the ratio of their …
- WAEC 2012 · Paper 2 · Q11In the diagram, is a rectangular garden long and wide. A wire mesh long is used …
- WAEC 2012 · Paper 2 · Q2Sonny is twice as old as Wale. Four years ago, he was four times as old as Wale. When will the sum of their ages be 66?
- WAEC 2012 · Paper 2 · Q6A boy had dalasis (D). He spent D15 and shared the remainder equally with his sister. If the sister's share was equal to of , …
- WAEC 2011 · Paper 2 · Q2Make the subject of the relation .
- WAEC 2010 · Paper 2 · Q2The angle of depression of a boat from the mid-point of a vertical cliff is . If the boat is from the foot of the cliff, …
- WAEC 2010 · Paper 2 · Q2(i) Solve the inequality . (ii) Illustrate the solution on a number line.
- WAEC 2009 · Paper 2 · Q6If , and , evaluate .
- WAEC 2009 · Paper 2 · Q9Simplify .
- WAEC 2009 · Paper 2 · Q2Solve the equation .
- WAEC 2008 · Paper 2 · Q4Solve the equation .
- WAEC 2008 · Paper 2 · Q6If and , find the values of and .
Objective (58)
- WAEC 2025 · Paper 1 · Q18Solve and . Use your result to find .
- NECO 2024 · Paper 1 · Q19Solve the equation .
- WAEC 2024 · Paper 1 · Q12If and , find the value of .
- WAEC 2024 · Paper 1 · Q17A number is added to both the numerator and the denominator of the fraction . If the result is , find the number.
- WAEC 2024 · Paper 1 · Q36The perimeter of a rectangular garden is . If the width is less than the length, find the length of the garden.
- WAEC 2024 · Paper 1 · Q41Two opposite sides of a rectangle are and . If an adjacent side is , find, in , …
- NECO 2023 · Paper 1 · Q18If 1 is added to the denominator of a fraction, the fraction becomes . When 3 is added to both the numerator and the denominator, it …
- NECO 2023 · Paper 1 · Q29Solve the simultaneous equations , .
- WAEC 2023 · Paper 1 · Q12One-third of the sum of two numbers is 12, and twice their difference is 12. Find the numbers.
- WAEC 2023 · Paper 1 · Q39If and , evaluate .
- WAEC 2023 · Paper 1 · Q7Mr Manu is 4 times as old as his son, Adu; 7 years ago the sum of their ages was 76. How old is Adu?
- WAEC 2022 · Paper 1 · Q13If and , what is the value of ?
- WAEC 2022 · Paper 1 · Q17Find the value of such that .
- WAEC 2021 · Paper 1 · Q13If and , find the value of .
- WAEC 2021 · Paper 1 · Q32A cyclist moved at a speed of for 2 hours. He then increased his speed by for the next 3 hours. If the total …
- WAEC 2021 · Paper 1 · Q42500 tickets for a concert were sold to adults and children at $4.50 and $3.00 respectively. If the total receipts were $1,987.50, how many adult tickets were sold?
- WAEC 2021 · Paper 1 · Q47A man will be years old in 8 years' time. If 2 years ago he was 63 years old, find the value of .
- WAEC 2021 · Paper 1 · Q9Mensah is 5 years old and Joyce is thrice as old as Mensah. In how many years will Joyce be twice as old as Mensah?
- WAEC 2020 · Paper 1 · Q10Given that and , calculate the value of .
- WAEC 2020 · Paper 1 · Q10Solve and simultaneously.
- WAEC 2020 · Paper 1 · Q17Two buses start from the same station at 9.00 am and travel in opposite directions along the same straight road. The first bus travels at …
- WAEC 2020 · Paper 1 · Q22A man is five times as old as his son. In four years' time, the product of their ages would be 340. If the son's age is , express the product …
- WAEC 2019 · Paper 1 · Q16If and , find the value of .
- WAEC 2019 · Paper 1 · Q3Solve .
- JAMB 2016 · UTME · Q26Given that and , solve for and respectively.
- JAMB 2016 · UTME · Q36If and , find .
- JAMB 2015 · UTME · Q17Find a two-digit number such that three times the tens digit is 2 less than twice the units digit, and twice the number is 20 greater than the …
- JAMB 2014 · UTME · Q22Find if .
- JAMB 2012 · UTME · Q13Solve for and in the equations and .
- JAMB 2011 · UTME · Q15Solve for and respectively in the simultaneous equations , .
- JAMB 2011 · UTME · Q43The sum of four consecutive integers is 34. Find the least of these numbers.
- JAMB 2010 · UTME · Q16Solve for and if and .
- JAMB 2010 · UTME · Q24If and are two non-zero numbers and , which of the following must be true?
- JAMB 2003 · UME · Q16Find the values of and respectively if and .
- JAMB 2003 · UME · Q21Three consecutive terms of a geometric progression are , and . Find the common ratio.
- JAMB 2002 · UME · Q35If is the solution of the equation , find the value of .
- JAMB 2001 · UME · Q10Solve the equations and .
- JAMB 1999 · UME · Q2Find the value of if .
- JAMB 1999 · UME · Q20The sum of two numbers is twice their difference. If the difference of the numbers is , find the larger of the two numbers.
- JAMB 1997 · UME · Q12Solve the simultaneous equations and .
- JAMB 1994 · UME · Q14If and , solve for in the equation .
- JAMB 1994 · UME · Q15Solve for in the equation .
- JAMB 1993 · UME · Q14Solve the simultaneous equations and for .
- JAMB 1993 · UME · Q33The three sides of an isosceles triangle are of lengths , and . Calculate .
- JAMB 1992 · UME · Q13A man invested a sum of ₦280.00 partly at and partly at . If the total interest is ₦12.80 per annum, find the amount invested at .
- JAMB 1991 · UME · Q20Find the two values of which satisfy the simultaneous equations and .
- JAMB 1991 · UME · Q31The angles of a quadrilateral are , , and . Find the smallest of these angles.
- JAMB 1989 · UME · Q23Solve the pair of equations and for and respectively.
- JAMB 1988 · UME · Q21Given that and , the value of is
- JAMB 1987 · UME · Q23Find two values of which satisfy the simultaneous equations and .
- JAMB 1986 · UME · Q12In 1984, Ike was 24 years old and his father was 45 years old. In what year was Ike exactly half his father's age?
- JAMB 1986 · UME · Q25If and , find .
- JAMB 1985 · UME · Q23Solve for : and .
- JAMB 1985 · UME · Q24Solve the simultaneous equations .
- JAMB 1985 · UME · Q9John gives one third of his money to Janet, who has ₦105.00. He then finds that his money is reduced to one-fourth of what Janet now has. Find …
- JAMB 1983 · UME · Q12In a class of 60 pupils, the numbers offering Biology, History, French, Geography and Additional Mathematics are shown in the pie chart. How …
- JAMB 1983 · UME · Q24Solve the simultaneous equations and for .
- JAMB 1983 · UME · Q4Solve the equations .