Solving more complex simultaneous equations by elimination | Maths

Starter quiz

Which equation is true for $x = 3$ and $y = -2$ ?

$3x + 8y = -7$ ✓

$2x + y = -8$

$x + 3y = 0$
If I add together the pair of simultaneous equations $4x + ay = 12$ and $5x - ay = 26$ , what is the resulting equation?

'9x = 38' ✓
Which equation is true for $x = \frac{1}{2}$ and $y = 2$ ?

$4x + 4y = 8$

$4x + y = 4$ ✓

$x^2 + y = 3$
If I add together the pair of simultaneous equations $x + y = 28$ and $x - y = 12$ , what is the resulting equation?

'2x = 40' ✓
Which equation is true for $x = -5$ and $y = -2$ ?

$x + 2 = y$

$2x + 2 = 4y$ ✓

$5x + 2 = 11y$
If I add together the pair of simultaneous equations $2x - 3y = 30$ and $y -2x = 6$ , what is the resulting equation?

'-2y = 36' ✓

Exit quiz

Which multiplier would match the y coefficients for equations 1) $15x + 4y = 12$ and 2) $2x + 2y = 6$ :

multiply equation 1) by 2

multiply equation 2) by 2 ✓

multiply equation 2) by 7
Which multiplier would match the x coefficients for equations 1) $3x + 5y = 21$ and 2) $x + 2y = 8$ :

multiply equation 1) by 2

multiply equation 1) by 3

multiply equation 2) by 3 ✓

multiply equation 2) by 5
Which multiplier would match coefficients for either $x$ or $y$ for equations 1) $5x + 4y = -13$ and 2) $10x + 2y = -44$ :

multiply equation 1) by 2 ✓

multiply equation 2) by 2 ✓

multiply equation 1) by 3

multiply equation 2) by 5
What is the value of $y$ for simultaneous equations $x + 4y = 7$ and $2x + 3y = -1$

'3' ✓
What is the value of $y$ for simultaneous equations $3x + 4y = 10$ and $2x + 2y = 4$

'4' ✓
What is the value of $x$ for simultaneous equations $3x + 3y = 21$ and $2x + y = 9$

'2' ✓

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Lesson Details

Key learning points

Additively combining the equations does not eliminate one variable unless the coefficients are the same.
Equivalent equations should be formed so the coefficients of one variable are the same (if not already).
When considering the coefficients, use your knowledge of LCM to help.

Common misconception

Forgetting to multiply every term in the equation when scaling or not multiplying every term by the same value.

Remind pupils that in order to maintain equality, the entire expression on both sides of the equals sign must be multiplied by the same value. Clear working and checking solutions can help pupils spot when they have made this mistake.

Keywords

Simultaneous equations - Equations which represent different relationships between the same variables are called simultaneous equations.
Elimination - Elimination is a technique to help solve equations simultaneously and is where one of the variables in a problem is removed.