Solving simultaneous linear equations by substitution | Maths

Starter quiz

Which multiplier would match the y coefficients for equations 1) $15x + 2y = a$ and 2) $2x + 6y = b$ :

multiply equation 1) by 2

multiply equation 2) by 2

multiply equation 2) by 7

multiply equation 1) by 3 ✓
Which multiplier would match the y coefficients for equations 1) $12x + 8y = a$ and 2) $2x + y = b$ :

multiply equation 1) by 2

multiply equation 1) by 6

multiply equation 2) by 8 ✓

multiply equation 2) by 2
Which multiplier would match the y coefficients for equations 1) $3x + 4y = a$ and 2) $6x + 12y = b$ :

multiply equation 2) by 3

multiply equation 2) by 2

multiply equation 1) by 2

multiply equation 1) by 3 ✓
What is the value of $y$ for simultaneous equations $2x + 8y = 14$ and $2x + 3y = -1$

'3' ✓
What is the value of $y$ for simultaneous equations $3x + 4y = 10$ and $8x + 8y = 16$

'4' ✓
What is the value of $x$ for simultaneous equations $9x + 9y = 63$ and $2x + y = 9$

'2' ✓

Exit quiz

Using substitution, what is the value of $x$ for simultaneous equations $3x + 2y = 16$ and $x + 3y = 17$ ?

'2' ✓
Using substitution, what is the value of $x$ for simultaneous equations $3x + 2y = 32$ and $x + 3y = 34$ ?

'4' ✓
Using substitution, what is the value of $y$ for simultaneous equations $5x + 4y = 28$ and $x + 3y = 10$ ?

'2' ✓
Using substitution, what is the value of $y$ for simultaneous equations $7x + 2y = 3$ and $2x + y = 3$ ?

'5' ✓
Using substitution, what is the value of $y$ for simultaneous equations $7x + 2y = 36$ and $2x + y = 15$ ?

'11' ✓
Using substitution, what is the value of $y$ for simultaneous equations $2y - 2x = -2$ and $3x + y = 19$ ?

'4' ✓

Worksheet

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Lesson Details

Key learning points

You can use your knowledge of changing the subject to rewrite one or both equations.
If one of the variables is the subject, the equivalent expression can be substituted into the other equation.
This is another method that involves reducing the number of variables.

Common misconception

Incorrectly expanding brackets or not using brackets when one expression is substituted into another.

Pupils should always use brackets when substituting. Remind them of the distributive law and that multiplying a negative value by a negative value gives a positive value. Checking final answers should catch these mistakes.

Keywords

Elimination - Elimination is a technique to help solve equations simultaneously and is where one of the variables in a problem is removed.
Substitution - Substitute means to put in place of another. In Algebra, substitution can be used to replace variables with values, terms, or expressions.
Subject (equation/formula) - The subject of an equation/a formula is a variable that is expressed in terms of other variables. It should have an exponent of 1 and a coefficient of 1