New
New
Year 10
Foundation

Solving more complex simultaneous equations by elimination

I can solve two complex linear simultaneous equations algebraically using elimination.

New
New
Year 10
Foundation

Solving more complex simultaneous equations by elimination

I can solve two complex linear simultaneous equations algebraically using elimination.

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Lesson details

Key learning points

  1. Additively combining the equations does not eliminate one variable unless the coefficients are the same.
  2. Equivalent equations should be formed so the coefficients of one variable are the same (if not already).
  3. When considering the coefficients, use your knowledge of LCM to help.

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.

Common misconception

Forgetting to multiply every term in the equation when scaling or not multiplying every term by the same value.

Remind pupils that in order to maintain equality, the entire expression on both sides of the equals sign must be multiplied by the same value. Clear working and checking solutions can help pupils spot when they have made this mistake.

Starting from the concrete with examples such as orders in a coffee shop can help students see why multiplying one equation works. They can verbalise to a partner why doubling the variables and doubling the cost maintains equality.
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).

Lesson video

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6 Questions

Q1.
Which equation is true for $$x = 3$$ and $$y = -2$$?
Correct answer: $$3x + 8y = -7$$
$$2x + y = -8$$
$$x + 3y = 0$$
Q2.
If I add together the pair of simultaneous equations $$4x + ay = 12$$ and $$5x - ay = 26$$, what is the resulting equation?
Correct Answer: 9x = 38
Q3.
Which equation is true for $$x = \frac{1}{2}$$ and $$y = 2$$?
$$4x + 4y = 8$$
Correct answer: $$4x + y = 4$$
$$x^2 + y = 3$$
Q4.
If I add together the pair of simultaneous equations $$x + y = 28$$ and $$x - y = 12$$, what is the resulting equation?
Correct Answer: 2x = 40
Q5.
Which equation is true for $$x = -5$$ and $$y = -2$$?
$$x + 2 = y$$
Correct answer: $$2x + 2 = 4y$$
$$5x + 2 = 11y$$
Q6.
If I add together the pair of simultaneous equations $$2x - 3y = 30$$ and $$y -2x = 6$$, what is the resulting equation?
Correct Answer: -2y = 36

6 Questions

Q1.
Which multiplier would match the y coefficients for equations 1) $$15x + 4y = 12$$ and 2) $$2x + 2y = 6$$:
multiply equation 1) by 2
Correct answer: multiply equation 2) by 2
multiply equation 2) by 7
Q2.
Which multiplier would match the x coefficients for equations 1) $$3x + 5y = 21$$ and 2) $$x + 2y = 8$$:
multiply equation 1) by 2
multiply equation 1) by 3
Correct answer: multiply equation 2) by 3
multiply equation 2) by 5
Q3.
Which multiplier would match coefficients for either $$x$$ or $$y$$ for equations 1) $$5x + 4y = -13$$ and 2) $$10x + 2y = -44$$:
Correct answer: multiply equation 1) by 2
Correct answer: multiply equation 2) by 2
multiply equation 1) by 3
multiply equation 2) by 5
Q4.
What is the value of $$y$$ for simultaneous equations $$x + 4y = 7$$ and $$2x + 3y = -1$$
Correct Answer: 3, y = 3
Q5.
What is the value of $$y$$ for simultaneous equations $$3x + 4y = 10$$ and $$2x + 2y = 4$$
Correct Answer: 4, y = 4
Q6.
What is the value of $$x$$ for simultaneous equations $$3x + 3y = 21$$ and $$2x + y = 9$$
Correct Answer: 2, x = 2