Forming and Solving Equations
Forming and solving equations means translating a word problem or diagram into an algebraic equation using a letter for the unknown value, then solving that equation to find the answer. It is a core GCSE Algebra skill used throughout the exam papers, for example with perimeters, angles, ages and shared totals, and usually finishes by checking the answer makes sense in the context of the question.
Before you start
Make sure you're comfortable with these topics first:
Method
- Choose a letter to represent the unknown quantity and write down clearly what it stands for.
- Translate the words or diagram into an algebraic expression or equation, using the given information, for example three more than double a number becomes 2x + 3.
- If two expressions are equal, such as two sides of a shape or a total, set them equal to each other to form the equation.
- Solve the equation using the balance method: do the same operation to both sides until the letter is isolated.
- Answer the actual question asked, which may require substituting your solution back into an expression, for example to find an angle or a length, not just stating the value of the letter.
- Check your answer fits the context, for example that lengths and ages are positive.
Worked example
A triangle has angles of x degrees, (x + 20) degrees and (2x - 10) degrees. Form an equation in x and solve it to find the size of each angle.
- Angles in a triangle sum to 180 degrees, so x + (x + 20) + (2x - 10) = 180.
- Simplify the left-hand side: 4x + 10 = 180.
- Subtract 10 from both sides: 4x = 170.
- Divide both sides by 4: x = 42.5.
- Substitute back into each expression: the three angles are 42.5, 62.5 and 75 degrees.
Practice questions
Try each question, then tap to reveal the answer.
Exam-style questions
Written in the style of a GCSE Maths exam paper, with a full mark scheme.
Solve 4(2x - 3) = 5x + 6.
A quadrilateral has angles of (x + 5) degrees, (x + 15) degrees, (2x - 5) degrees and (2x + 15) degrees. (a) Form an equation in x and solve it. (3) (b) Work out the size of the largest angle in the quadrilateral. (2)
At a craft fair, 5 keyrings and 2 magnets cost 8.60 pounds in total. 5 keyrings and 4 magnets cost 11.20 pounds in total. Let x pounds be the cost of one keyring and y pounds be the cost of one magnet. (a) Write down a pair of simultaneous equations in x and y. (2) (b) Solve your equations to find the cost of one keyring and the cost of one magnet. (2)
Free printable worksheet
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