GCSE Maths · Higher · Chapter 15: Equations and inequalities · Lesson 2

Simultaneous equations algebraically

Grades 5–8About 55 minutesCalculator allowed49 marks

Hints online, answers free with an account:
mathswariz.uk/worksheets/gcse-simultaneous-equations-algebraically/

NameClassDate

Do Now

Grades 4–6

The first question is what today's lesson needs. The others bring back earlier topics.

A1
Needed today
Solve $5 x - 2 = 3 x + 2$ .
[1 mark]
Answer
A2
From chapter 13
P(win) $= 0.15$ . How many wins would you expect in 200 games?
[1 mark]
Answer
A3
Key Stage 3
Round $2.547$ to 1 decimal place.
[1 mark]
Answer
A4
Key Stage 3
Work out $(- 4) \times (- 5)$ .
[1 mark]
Answer

Grades 5–6

Your teacher works through each example with you. Then try the one beside it.

Example 1

Solve the simultaneous equations $3 x + y = 17$ and $5 x - y = 15$ .

Hint The

y

terms have opposite signs, so add the equations.

B1
Solve the simultaneous equations $4 x + 3 y = 25$ and $4 x - 2 y = 10$ .
[3 marks]
Answer

Example 2

Solve the simultaneous equations $y = 3 x - 2$ and $5 x - y = 8$ .

Hint Put

3 x - 2

in place of

y

, in a bracket.

B2
Solve the simultaneous equations $y = 3 - 2 x$ and $3 x + 2 y = 4$ .
[3 marks]
Answer

Example 3

Solve the simultaneous equations $2 x + 5 y = 1$ and $x + 3 y = 0$ .

Hint Multiply the second equation by

2

so both have

2 x

B3
Solve the simultaneous equations $5 x + 3 y = 11$ and $3 x - 2 y = 18$ . You must show your working.
[4 marks]
Answer

Grades 5–7

C1
Solve the simultaneous equations $3 x = 2 y + 7$ and $4 y = 5 x - 13$ .
[3 marks]
Answer
C2
Solve the simultaneous equations $0.5 x + 0.2 y = 3.1$ and $0.3 x - 0.2 y = 1.7$ .
[3 marks]
Answer

C3
The lines $y = 3 x - 4$ and $2 x + y = 11$ meet at $P$ . Find the coordinates of $P$ .
[3 marks]
Not drawn accurately
Answer
C4
Solve the simultaneous equations $\frac{x}{2} + \frac{y}{3} = 4$ and $x - y = 3$ .
[3 marks]
Answer
C5
The $n$ th term of a sequence is $an + b$ . The 4th term is $19$ and the 9th term is $44$ . Work out the 20th term.
[3 marks]
Answer
C6
Explain why $3 x - 2 y = 5$ and $6 x - 4 y = 7$ cannot both be true.
[2 marks]

Grades 6–8

D1
Raj solves $5 x + 2 y = 16$ and $3 x - 2 y = 8$ . He writes, "I subtract the equations, so $2 x = 8$ and $x = 4$ ."
Explain what Raj has done wrong, and solve the equations correctly.
[3 marks]

Grade 8 and beyond

No route is given. The hints are at the end of the sheet. Use one at a time.

Colour one circle on each line.

	Not yet	Nearly	Yes
I can solve by adding or subtracting.
I can solve by substituting.
I can multiply first to match a term.

The worked answers and the full mark scheme are free with a Mathswariz account. Teachers and students can both sign up.