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

Starter quiz

Which of these is not a solution for simultaneous equations $2x^2 + 8y = 34$ and $x - 2y = -1$ ?

$(-5, -2)$

$(3, 2)$

$(5, 3)$ ✓
Write the positive coordinate solution for $2x^2 + 6y = 38$ and $x - y = -3$

'(2,5)' ✓
What is the negative value of $x$ for $4x^2 + 8x - 12 = 0$

'-3' ✓
What is the value of $x$ for $4x^2 + 8x + 4 = 0$

'- 1' ✓
What is the negative value of $x$ for $6x^2 + 12x - 18 = 0$

'-3' ✓
What is the positive value of $x$ for $2x^2 + 6x - 8 = 0$

'1' ✓

Exit quiz

If equation A is $x^2 + 3y = 24$ and equation B is $4x - 3y = -3$ , which coordinate pair would sit in A and not B?

$(3, 5)$

$(6, -4)$ ✓

$(0, 6)$
If equation A is $x - 5y = -7$ and equation B is $x^2 + y^2 = 13$ , which coordinate pair would sit in A and not B?

$(-2, 1)$ ✓

$(3, 2)$

$(0, 4)$
If equation A is $x^2 + 4y = 68$ and equation B is $x - 4y = 4$ , which coordinate pair would sit in the intersection of A and B?

$(2, 16)$

$(6, 8)$

$(8, 1)$ ✓
What is the positive coordinate pair that solves both $x^2 + y^2 = 17$ and $x - y = 3$ ?

'(4,1)' ✓
What is the positive coordinate pair that solves both $x^2 + y^2 = 40$ and $x - y = 4$ ?

'(6,2)' ✓
What is the positive coordinate pair that solves both $x^2 + y^2 = 13$ and $x - y = -1$ ?

'(2,3)' ✓

Worksheet

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Lesson Details

Key learning points

Consider which variable to make the subject for the substitution.
Depending which variable you chose, you may need to expand a pair of bracketed expressions.
Your choice may make the substitution significantly easier.

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

Substitution - Substitute means to put in place of another. In algebra, substitution can be used to replace variables with values, terms, or expressions.