Solving algebraic simultaneous equations by elimination | Maths

Starter quiz

If ◉ ◉ ◯ = 14 points and ◉◉ ◯ ◯ = 16 points, what is the value of ◉?

'6' ✓
If ◉◉◯ = 15 points and ◉◯◯ = 12 points, what is the value of ◉?

'6' ✓
Given that ◉◉◯◯ = 20 points and ◯◯◯◉ = 22 points, what is the value of ◉?

'4' ✓
Assuming ◉◯ = 9 points and ◉◉◯◯◯ = 25 points, what is the value of ◉?

'2' ✓
Which equation is true for $x = 5$ and $y = 1$ ?

$2x + y = -8$

$2x + y = 11$ ✓

$2x + y = 4$
When ◉◉◯◯◯ = 28 points and ◉◉◉◯ = 28 points, what is the value of ◉?

'8' ✓

Exit quiz

Multiply this equation by $4$ : $3x + 10 = 40$

'12x + 40 = 160' ✓
Multiply this equation by $3$ : $20 + 2y = 16$

'60 + 6y = 48' ✓
Multiply this equation by $4$ : $5x + 10y = 100$

$20x + 10y = 400$

$9x + 14y = 104$

$20x + 40y = 400$ ✓
Which of these steps would match the y coefficients for equations 1) $3x + 4y = 45$ and 2) $5x + 8y = 83$ :

double equation 1 ✓

add both equations together

double equation 2
What is the value of x for $4x + 4y = 28$ and $3x + 8y = 36$ ?

$x = 4, y = 3$ ✓

$x = 5, y = 2$

$x = 3, y = 4$
What is the value of x for equations $3x + 4y = 33$ and $x + 3y = 16$ ?

'7' ✓

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Lesson Details

Key learning points

It is possible to find a solution that satisfies two equations with two unknowns by trial and error.
A more efficient method is to combine the two equations to create a third valid equation .
If the third equation contains only one unknown, it is easy to solve .
Once you know one of the unknowns, you can substitute to find the other .

Common misconception

Performing different operations on different variables. E.g. subtracting one variable to eliminate then adding the other variable and constant. Pupils incorrectly think they are adding to eliminate.

This is caused by negative number skills. Subtracting two identical values always gives zero even if both are negative. If a term is the same in both equations, we subtract to eliminate. Clear working is crucial here.

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.