New

Year 11

Higher

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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New

Year 11

Higher

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.

Download all resources

Share activities with pupils

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Lesson details

Key learning points

You can use your knowledge of linear graphs to draw the graphs of both equations on the same axes
If there exists a solution, the point of intersection is that solution
If the lines are parallel then there are no solutions
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 (2024), licensed on Open Government Licence version 3.0 except where otherwise stated. See Oak's terms & conditions (Collection 2).

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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 $$2y+5x=10$$ ?

$$-\frac{2}{5}$$

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 $$2y=6-4x$$ ?

Correct Answer: An image in a quiz

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?

$$x=0, y=1$$

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 $$y=2x-4$$?

$$x=0, y=-4$$

$$x=1, y=0$$

$$x=2, y=1$$

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 $$3y+2x=12$$?

$$x=0, y=-1$$

$$x=1, y=0$$

$$x=2, y=1$$

Correct answer: $$x=3, y=2$$

$$x=4, y=3$$