Combining equations | Maths | Quizalize & Oak National Academy

Starter quiz

Which pair of coordinates does not satisfy the equation $y = 2x + 4$ ?

(1, 6)

(2, 8)

(3, 10)

(4, 11) ✓
The area of a rectangle is $90 cm^2$ . The perimeter is $94 cm$ . Which two equations are true for side lengths $a$ and $b$ ?

$ab = 90$ ✓

$a + b = 94$

$2(a + b) = 94$ ✓

$ab = 94$
Which two of the following are correct for a right triangle with sides $a, b$ and hypotenuse $c$ ?

$a + b + c = abc$

$Area = \frac{ab}{2}$ ✓

$Perimeter = a + b + c$ ✓

$Area = ab$
If $x = -9$ , what is the value of $y$ for $x + 2y = 13$ ?

'11' ✓
Which pair of coordinates does not satisfy the equation $y = -3x + 2$ ?

(-1, 5)

(0, 2)

(1, 1) ✓

(2, -4)
There are 12 goals scored in a football match. Team A scored $a$ goals, and winning Team B scored $b$ goals. The winning team scored 5 more than the losing team.

$a + b = 12$ ✓

$a + b = 5$

$a = b - 5$ ✓

$a = b - 5$ ✓

Exit quiz

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

$2x + y = -8$

$2x + 3y = 19$ ✓

$4x + 2y = 20$
Which equation is true for $x = 3$ and $y = 9$ ?

$2x + 3y = 12$

$3x + y = 16$

$2(x + y) = 24$ ✓
Which equation is true for $x = -2$ and $y = 3$ ?

$3y - x = 11$ ✓

$3y - x = 7$

$3x - y = 9$
Which equation is true for $x = 8$ and $y = 1$ ?

$x^2 - y^2 = 64$

$x^2 = 34y$

$x^2 + y = 65$ ✓
If I add together the pair of simultaneous equations $5x + 7y = 87$ and $7x + 7y = 91$ , what is the resulting equation?

'12x + 14y = 178' ✓
If I add together the pair of simultaneous equations $5x + 2y = 10$ and $7x - 2y = -50$ , what is the resulting equation?

'12x = -40' ✓

Worksheet

Loading worksheet ...

Presentation

Loading presentation ...

Video

Lesson Details

Key learning points

Two equations can be combined into a third equation.
You can combine equations using the standard arithmetic operations.
The new equation may not contain both variables any more.

Common misconception

Mistakes can be made when subtracting negative values. E.g. thinking that 5 - - 2 = 3.

Consider additive inverses, subtracting a negative is the same as adding the additive inverse. Pupils should be able to spot mistakes in learning cycle 1 by checking their new equation is still true.

Keywords

Elimination - Elimination is a technique to help solve equations simultaneously and is where one of the variables in a problem is removed.