Solving a quadratic and linear pair of simultaneous equations using elimination | Maths

Starter quiz

If A and B are simultaneous equations such that A: $2x + 4y = 42$ and B: $3x + y = 43$ where will coordinate pair $(1, 10)$ go in the Venn diagram?

In B but not A

In A but not B ✓

The intersection A and B

Outside of both A and B
If A and B are simultaneous equations such that A: $4x + 4y = 20$ and B: $6x + 2y = 14$ where will coordinate pair $(1, 4)$ go in the Venn diagram?

The intersection A and B ✓

In B but not A

In A but not B

Outside of both A and B
If A and B are simultaneous equations such that A: $2y - 2x = 8$ and B: $9x + 3y = 12$ where will coordinate pair $(0, 0)$ go in the Venn diagram?

In A but not B

In B but not A

The intersection A and B

Outside of both A and B ✓
If A and B are simultaneous equations such that A: $3x + y = 40$ and B: $14x + 2y = 176$ where will coordinate pair $(12, 4)$ go in the Venn diagram?

In A but not B

In B but not A

The intersection A and B ✓

Outside of both A and B
If A and B are simultaneous equations such that A: $6x + 2y = 26$ and B: $7x + 6y = 34$ where will coordinate pair $(5, -2)$ go in the Venn diagram?

In A but not B ✓

In B but not A

The intersection A and B

Outside of both A and B
If A and B are simultaneous equations such that A: $6x = 18 - 2y$ and B: $8x +6y = 14$ where will coordinate pair $(1, 1)$ go in the Venn diagram?

In A but not B

In B but not A ✓

The intersection A and B

Outside of both A and B

Exit quiz

What is the positive value of $x$ for $x^2 + 3x - 4 = 0$

'1' ✓
What is the value of $x$ for $2x^2 + 4x + 2 = 0$

'-1' ✓
What is the negative value of $x$ for $2x^2 + 4x - 6 = 0$

'-3' ✓
Write the positive coordinate solution for $x^2 + 3y = 19$ and $3x - 3y = -9$

'(2,5)' ✓
Write the positive coordinate solution for $x^2 + 2y = 11$ and $3x - 2y = 7$

'(3,1)' ✓
Which of these is not a solution for simultaneous equations $x^2 + 4y = 17$ and $2x - 4y = -2$ ?

$(-5, -2)$

$(5, 3)$ ✓

$(3, 2)$

Worksheet

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Lesson Details

Key learning points

When one equation is quadratic it will only be possible to eliminate the linear variable.
Doing so produces a third equation which is quadratic.
You can use any of your methods for solving a quadratic to find possible solutions.
These values need to be substituted into one of the original equations to find its pair.
If your quadratic has two valid solutions then you will have two pairs of solutions to your simultaneous equations.

Common misconception

Pupils find the two $x$ values after solving the combined quadratic and declare that the solution.

It is important to substitute both $x$ values back in to one of the original equations to find the corresponding $y$ values. Without these, the solutions are incomplete.

Keywords

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