Simultaneous Equations: WJEC GCSE Intermediate June 2022 Unit 1 Q16

Intermediate June 2022 Unit 1 Q16

WJECIntermediateCurrent spec4 marksSimultaneous Equations

16. Solve the following simultaneous equations using an algebraic (not graphical) method.
You must show all your working. [4]

\[\begin{aligned} 2x + 3y &= 29 \\ 5x - 4y &= -8 \end{aligned}\]

Mark scheme

Scheme	Marks	Comments
Method to eliminate one variable e.g. ‘equal coefficients AND appropriate intention to add or subtract’ or use a method of substitution	M1	Allow one error in one term (not the term with equal coefficients).
First variable found \(x = 4\) or \(y = 7\).	A1	CAO. Award A0 for an answer that leads to a whole number, but not expressed as a whole number (e.g. \(y\) = 161/23 or \(x\) = 92/23)
Substitute to find the 2^nd variable. Second variable found.	m1 A1	FT substitution of their ‘1^st variable’ if M1 gained. If FT leads to a whole number answer, it must be shown as a whole number. Otherwise accept a fraction. If no marks gained, allow SC1 for both answers of \(x = 4\) AND \(y = 7\).