Equations which represent different relationships between the same variables are called simultaneous equations.

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

Solving algebraic simultaneous equations by elimination

Maths

Checking and securing understanding of interpreting graphs

Forming simultaneous equations

Combining equations

Solving simultaneous equations by elimination from a context

Solving more complex simultaneous equations by elimination

Solving simultaneous linear equations by substitution

Solving simultaneous linear equations graphically

Solving a quadratic and linear pair of simultaneous equations using elimination

Solving a quadratic and linear pair of simultaneous equations using substitution

Solving a quadratic and linear pair of simultaneous equations graphically

Solving simultaneous equations via any method

Problem solving with linear and quadratic simultaneous equations

In the future unit, pupils will learn how to extend their understanding of solving equations and extend this to consider inequalities. Pupils will consider a variety of inequalities and ways that their solutions can be represented.

In the prior unit, pupils learnt to solve quadratic equations by factorising and this skill will be required in this unit through manipulating two simultaneous equations to find the solutions. For pupils studying the higher content, solving quadratic equations is required if one of the simultaneous equations is a quadratic.

In this unit pupils will learn to solve a pair of simultaneous equations from different starting points and cases using a variety of strategies.

Simultaneous equations: 2 variables

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

Multiply this equation by $$3$$: $$20 + 2y = 16$$

Multiply this equation by $$4$$: $$5x + 10y = 100$$

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

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

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

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

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

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

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

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

When ◉◉◯◯◯ = 28 points and ◉◉◉◯ = 28 points, what is the value of ◉?

Starter Quiz

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