AQA · Mathematics · 8300
GCSE Maths: Simultaneous equations (elimination)
Algebra · AQA GCSE Maths (8300). Cards are generated from the Corbettmaths textbook exercise and practice questions for Simultaneous equations (elimination) (Corbettmaths Video 295), and every card links back to the exact page it came from. Practice tests generate fresh variations of these questions, so the numbers change every attempt. Source material © Corbettmaths — used with attribution.
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What is the elimination method for solving simultaneous equations?
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A technique where you add or subtract equations to eliminate one variable, allowing you to solve for the other.
In elimination, when should you add the two equations together?
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When the coefficients of one variable are opposites (e.g., +y and −y), so they cancel out when added.
In elimination, when should you subtract one equation from the other?
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When the coefficients of one variable are the same (e.g., both +y), so they cancel out when subtracted.
To solve 5x + 3y = 41 and 2x + 3y = 20 by elimination, subtract the equations to eliminate ?
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y
What must you do if neither variable has matching or opposite coefficients in two simultaneous equations?
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Multiply one or both equations by suitable numbers to create matching or opposite coefficients for one variable.
When solving simultaneous equations by elimination, what do you do after eliminating one variable?
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Solve the resulting single-variable equation, then substitute the value back into one of the original equations to find the other variable.
Before using elimination on equations like x = 10 − y and 2x + y = 17, what must you do first?
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Rearrange them into standard form (with variables on one side and constant on the other), e.g., x + y = 10.
If coffee + tea = £4 and coffee + 3 teas = £7, how would you use elimination to find the price of tea?
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Subtract the first equation from the second to eliminate coffee, giving 2 teas = £3, so tea = £1.50.
To solve 3x + 5y = 1 and 2x − 3y = 7 by elimination, what is one way to eliminate x?
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Multiply the first equation by 2 and the second by 3 (giving 6x in both), then subtract to eliminate x.
When solving word problems with simultaneous equations, what quantity does each variable typically represent?
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Each unknown price, distance, or quantity in the problem. For example, the cost of one adult ticket or the length of one route.
What is the geometric meaning of solving a system of two linear equations in two variables?
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Finding the coordinates of the point where the two straight lines intersect.
When a word problem asks for a total cost or distance that's a multiple of the unit values, what should you do after solving for the unit values?
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Multiply the solved unit values by the required quantities and add them together to find the final answer.
In a simultaneous equations word problem, how do you form each equation?
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Express each given relationship or total as an equation using the variables. For example, '4 adult tickets and 1 child ticket for £120' becomes 4a + c = 120.
When solving simultaneous equations where one equation is already solved for a variable (e.g., y = 2x − 7), which method is most efficient?
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Substitution method. Replace the variable in the other equation with the expression given.
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