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      Checking and securing understanding of simultaneous equations

      I can recognise that the point of intersection of two linear graphs satisfies both relationships and hence represents the solution to both those equations.

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      Lesson 1 of 14
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      • Year 11

      Checking and securing understanding of simultaneous equations

      I can recognise that the point of intersection of two linear graphs satisfies both relationships and hence represents the solution to both those equations.

      Lesson details

      Key learning points

      1. You can use your knowledge of linear graphs to draw the graphs of both equations on the same axes
      2. If there exists a solution, the point of intersection is that solution
      3. If the lines are parallel then there are no solutions
      4. If the lines lie on top of each other, there are infinitely many solutions

      Keywords

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

      • Linear - The relationship between two variables is linear if, when plotted on a pair of axes, a straight line is formed.

      Common misconception

      Pupils may mix-up the x and y coordinates.

      Remind pupils that the x value is read from the x-axis and is read first. The y value is read from the y-axis and is read second.

      Give pupils more equations with fractional gradients and ask them to create a useful table of values for plotting. What x values should be chosen to generate integer co-ordinates? Can pupils generalise a rule?
      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

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      6 Questions

      Q1.
      Which of these are solutions to the equation $$y=3x-4$$?

      $$x=0, y=3$$
      Correct answer: $$x=2, y=2$$
      $$x=5, y=19$$
      $$x=8, y=18$$
      Correct answer: $$x=10, y=26$$

      Q2.
      What is the gradient of the line with equation $$y=4x+2$$ ?

      Correct Answer: 4, four

      Q3.
      What is the gradient of the line with equation $$2y+5x=10$$ ?

      2
      5
      10
      $$-\frac{2}{5}$$
      Correct answer: $$-\frac{5}{2}$$

      Q4.
      What is the $$x$$ intercept of the line with equation $$3y+4x=12$$ ?

      (0, 3)
      (0, 4)
      Correct answer: (3, 0)
      (4, 0)

      Q5.
      Fill in the missing coordinate for the $$y$$ intercept of the line with equation $$3y+4x=12$$ (0, )

      Correct Answer: 4

      Q6.
      Which of these shows the line with equation $$2y=6-4x$$ ?

      An image in a quiz
      An image in a quiz
      An image in a quiz
      Correct Answer: An image in a quiz
      An image in a quiz

      Assessment exit quiz

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      6 Questions

      Q1.
      The __________ shows us a value of $$x$$ and $$y$$ that satisfies two linear equations simultaneously when plotted.

      gradient
      $$x$$-intercept
      $$y$$-intercept
      Correct answer: point of intersection

      Q2.
      Here are the lines with equations $$y=2x+1$$ and $$y=5-2x$$. What is the solution to both equations simultaneously?

      An image in a quiz
      $$x=0, y=1$$
      Correct answer: $$x=1, y=3$$
      $$x=2.5, y=0$$
      $$x=3, y=1$$

      Q3.
      How many solutions are there to the equations $$y=2x+8$$ and $$y=2x+3$$ when solved simultaneously?

      Correct answer: none
      one
      two
      infinite

      Q4.
      How many solutions are there to the equations $$2y=3x+4$$ and $$4y-6x=8$$ when solved simultaneously?

      none
      one
      two
      Correct answer: infinite

      Q5.
      Here is the line with equation $$y=x-1$$. What is the solution to the simultaneous equations $$y=x-1$$ and $$y=2x-4$$?

      An image in a quiz
      $$x=0, y=-4$$
      $$x=1, y=0$$
      $$x=2, y=1$$
      Correct answer: $$x=3, y=2$$
      $$x=4, y=5$$

      Q6.
      Here is the line with equation $$y=x-1$$. What is the solution to the simultaneous equations $$y=x-1$$ and $$3y+2x=12$$?

      An image in a quiz
      $$x=0, y=-1$$
      $$x=1, y=0$$
      $$x=2, y=1$$
      Correct answer: $$x=3, y=2$$
      $$x=4, y=3$$

      Lesson appears in

      UnitMaths / Inequalities

      Maths

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