New
New
Year 10
Higher

Solving algebraic simultaneous equations by elimination

I can solve two linear simultaneous equations algebraically using elimination.

New
New
Year 10
Higher

Solving algebraic simultaneous equations by elimination

I can solve two linear simultaneous equations algebraically using elimination.

Lesson details

Key learning points

  1. It is possible to find a solution that satisfies two equations with two unknowns by trial and error.
  2. A more efficient method is to combine the two equations to create a third valid equation .
  3. If the third equation contains only one unknown, it is easy to solve .
  4. 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.

Pupils should be checking their answers satisfy both equations at every opportunity.
Teacher tip

Licence

This content is © Oak National Academy Limited (2024), licensed on Open Government Licence version 3.0 except where otherwise stated. See Oak's terms & conditions (Collection 2).

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6 Questions

Q1.
If ◉ ◉ ◯ = 14 points and ◉◉ ◯ ◯ = 16 points, what is the value of ◉?
Correct Answer: 6, 6 points
Q2.
If ◉◉◯ = 15 points and ◉◯◯ = 12 points, what is the value of ◉?
Correct Answer: 6
Q3.
Given that ◉◉◯◯ = 20 points and ◯◯◯◉ = 22 points, what is the value of ◉?
Correct Answer: 4
Q4.
Assuming ◉◯ = 9 points and ◉◉◯◯◯ = 25 points, what is the value of ◉?
Correct Answer: 2
Q5.
Which equation is true for $$x = 5$$ and $$y = 1$$?
$$2x + y = -8$$
Correct answer: $$2x + y = 11$$
$$2x + y = 4$$
Q6.
When ◉◉◯◯◯ = 28 points and ◉◉◉◯ = 28 points, what is the value of ◉?
Correct Answer: 8

6 Questions

Q1.
Multiply this equation by $$4$$: $$3x + 10 = 40$$
Correct Answer: 12x + 40 = 160
Q2.
Multiply this equation by $$3$$: $$20 + 2y = 16$$
Correct Answer: 60 + 6y = 48, 6y + 60 = 48
Q3.
Multiply this equation by $$4$$: $$5x + 10y = 100$$
$$20x + 10y = 400$$
$$9x + 14y = 104$$
Correct answer: $$20x + 40y = 400$$
Q4.
Which of these steps would match the y coefficients for equations 1) $$3x + 4y = 45$$ and 2) $$5x + 8y = 83$$:
Correct answer: double equation 1
add both equations together
double equation 2
Q5.
What is the value of x for $$4x + 4y = 28$$ and $$3x + 8y = 36$$ ?
Correct answer: $$x = 4, y = 3$$
$$x = 5, y = 2$$
$$x = 3, y = 4$$
Q6.
What is the value of x for equations $$3x + 4y = 33$$ and $$x + 3y = 16$$ ?
Correct Answer: 7, x = 7