Solve this simple pair of equations by substitution.
(a)Substitute y = 2x into x + y = 9 and solve for x, then find y.(3)
2
Solve the pair of equations using elimination.
(a)Eliminate x by subtracting the second equation from the first and find y, then x.(3)
3
Solve this pair by substitution where one equation is rearranged first.
(a)Rearrange 3x - y = 7 to express y in terms of x, substitute into x + 2y = 4 and solve.(3)
4
Solve by elimination after multiplying one equation.
(a)Multiply the first equation so you can eliminate x or y, then solve.(3)
5
A practical context. Solve by substitution.
(a)Write equations, substitute and find k and Yusuf's number.(4)
6
Solve the pair where elimination needs different multipliers.
(a)Use elimination by making coefficients of x or y equal and solve both values.(4)
Mark scheme · KS3.M-A17 Introduction to Simultaneous Equations
Question 1
(a) M1 substitution shown: x + 2x = 9 or equivalent
(a) M1 correct method to find x: 3x = 9, x = 3
(a) A1 correct y value y = 6 cao
(a) Answer: x = 3, y = 6
Question 2
(a) M1 correct elimination leading to 4y = 8 or equivalent
(a) M1 correct method to find y: y = 2
(a) A1 substitute to find x = 7/2 or 3.5 cao
(a) Answer: x = 7/2, y = 2
Question 3
(a) M1 rearrangement to get y = 3x - 7 and substitution into the second equation
(a) M1 correct algebra to a single equation in x, e.g. x + 2(3x - 7) = 4 giving 7x = 18
(a) A1 correct values x = 18/7 and y = 5/7 cao
(a) Answer: x = 18/7, y = 5/7
Question 4
(a) M1 multiply first equation by 3 to give 3x + 12y = 33 or equivalent
(a) M1 subtract the second equation correctly to find 14y = 32
(a) A1 y = 16/7 and x = 13/7 cao
(a) Answer: x = 13/7, y = 16/7
Question 5
(a) M1 correct equations: Yusuf = k + 3 and k + (k + 3) = 31 or equivalent
(a) M1 attempt to solve: 2k + 3 = 31 leading to 2k = 28
(a) M1 k = 14 found
(a) A1 Yusuf has 17 stamps cao
(a) Answer: Amina has 14 stamps, Yusuf has 17 stamps
Question 6
(a) M1 correct multiplication to make a coefficient equal, e.g. multiply first by 3 and second by 4 to eliminate x producing 12x + 15y = 6 and 12x - 8y = 44
(a) M1 correct elimination to find 23y = -38 or equivalent