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      Solving simultaneous linear equations by substitution

      I can solve two linear simultaneous equations algebraically using substitution.

      Lesson 7 of 13
      New
      New
      • Year 10

      Solving simultaneous linear equations by substitution

      I can solve two linear simultaneous equations algebraically using substitution.

      Lesson details

      Key learning points

      1. You can use your knowledge of changing the subject to rewrite one or both equations.
      2. If one of the variables is the subject, the equivalent expression can be substituted into the other equation.
      3. This is another method that involves reducing the number of variables.

      Keywords

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

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

      • Subject (equation/formula) - The subject of an equation/a formula is a variable that is expressed in terms of other variables. It should have an exponent of 1 and a coefficient of 1

      Common misconception

      Incorrectly expanding brackets or not using brackets when one expression is substituted into another.

      Pupils should always use brackets when substituting. Remind them of the distributive law and that multiplying a negative value by a negative value gives a positive value. Checking final answers should catch these mistakes.

      Pupils should be looking at key features of their equations to spot efficient methods. This can be linked to finding the intersection of two linear graphs. As they are often given in the form y = mx + c, substitution is an easy method to use (the two expressions can be equated).
      Teacher tip

      Licence

      This content is © Oak National Academy Limited (2025), 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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      Prior knowledge starter quiz

      6 Questions

      Q1.
      Which multiplier would match the y coefficients for equations 1) $$15x + 2y = a$$ and 2) $$2x + 6y = b$$:

      multiply equation 1) by 2
      multiply equation 2) by 2
      multiply equation 2) by 7
      Correct answer: multiply equation 1) by 3

      Q2.
      Which multiplier would match the y coefficients for equations 1) $$12x + 8y = a$$ and 2) $$2x + y = b$$:

      multiply equation 1) by 2
      multiply equation 1) by 6
      Correct answer: multiply equation 2) by 8
      multiply equation 2) by 2

      Q3.
      Which multiplier would match the y coefficients for equations 1) $$3x + 4y = a$$ and 2) $$6x + 12y = b$$:

      multiply equation 2) by 3
      multiply equation 2) by 2
      multiply equation 1) by 2
      Correct answer: multiply equation 1) by 3

      Q4.
      What is the value of $$y$$ for simultaneous equations $$2x + 8y = 14$$ and $$2x + 3y = -1$$

      Correct Answer: 3, y =3

      Q5.
      What is the value of $$y$$ for simultaneous equations $$3x + 4y = 10$$ and $$8x + 8y = 16$$

      Correct Answer: 4, y = 4

      Q6.
      What is the value of $$x$$ for simultaneous equations $$9x + 9y = 63$$ and $$2x + y = 9$$

      Correct Answer: 2, x = 2

      Assessment exit quiz

      6 Questions

      Q1.
      Using substitution, what is the value of $$x$$ for simultaneous equations $$3x + 2y = 16$$ and $$x + 3y = 17$$?

      Correct Answer: 2, x = 2

      Q2.
      Using substitution, what is the value of $$x$$ for simultaneous equations $$3x + 2y = 32$$ and $$x + 3y = 34$$?

      Correct Answer: 4, x = 4

      Q3.
      Using substitution, what is the value of $$y$$ for simultaneous equations $$5x + 4y = 28$$ and $$x + 3y = 10$$?

      Correct Answer: 2, y = 2

      Q4.
      Using substitution, what is the value of $$y$$ for simultaneous equations $$7x + 2y = 3$$ and $$2x + y = 3$$?

      Correct Answer: 5, y = 5

      Q5.
      Using substitution, what is the value of $$y$$ for simultaneous equations $$7x + 2y = 36$$ and $$2x + y = 15$$?

      Correct Answer: 11, y = 11

      Q6.
      Using substitution, what is the value of $$y$$ for simultaneous equations $$2y - 2x = -2$$ and $$3x + y = 19$$?

      Correct Answer: 4, y = 4

      Lesson appears in

      UnitMaths / Simultaneous equations: 2 variables