Year 9

Year 9

# Representing simultaneous equations graphically (Part 2)

## Lesson details

### Key learning points

1. In this lesson, we will learn to recognise simultaneous equations with no solutions by representing the equations on a graph.

### Licence

This content is made available by Oak National Academy Limited and its partners and licensed under Oak’s terms & conditions (Collection 1), except where otherwise stated.

## Video

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## Worksheet

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## Starter quiz

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### 5 Questions

Q1.
Fill in the gaps: We can use ____ to solve simultaneous equations.
Knowledge
Numbers
Terms
Q2.
What are the coordinates of the points of intersection for y = x + 5 and y = -2x - 1?
(-2, -3)
(2, -3)
(2, 3)
Q3.
Use a graph to solve y = x + 5 and y = -2x - 1 simultaneously.
x = -2, y = -3
Correct answer: x = -2, y = 3
x = 2, y = -3
x = 2, y = 3
Q4.
Create equations for the following statements: "I'm thinking of 2 numbers that have a sum of 3", "I'm thinking of 2 numbers. I triple the first number and add the second to get -1".
x + y = 3, 2x + y = -1
Correct answer: x + y = 3, 3x + y = -1
y = -x + 3, y = 3x - 1
y = x + 3, y = 3x - 1
Q5.
Find the values of x and y that are true for both of the following statements: "I'm thinking of 2 numbers that have a sum of 3", "I'm thinking of 2 numbers. I triple the first number and add the second to get -1".
x = -2, y = -5
Correct answer: x = -2, y = 5
x = 2, y = -5
x = 2, y = 5

## Exit quiz

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### 5 Questions

Q1.
Which of the following statements is true?
Simultaneous equations always have solutions.
Simultaneous equations can only be solved using graphs.
Correct answer: Simultaneous equations do not always have solutions.
Simultaneous equations never have solutions.
Q2.
Which of the following equations do not have solutions when solved simultaneously?
x + y = 2, y = x - 4
y = 2x + 1, y = -2x - 1
Correct answer: y = 3x - 2, y = 3x + 100
y = x + 3, y = 2x + 3
Q3.
Which of the following equations have a solution where the x coordinate is negative?
Correct answer: x - 2y = 6, y = -4
x - 2y = 6, y = 5 - 3x
y = 2x + 4, y = 5 - 3x
y = 5 - 3x, y = - 4
Q4.
Which of the following equations have a solution where both the coordinates are negative?
Correct answer: x - 2y = 6, y = -4
x - 2y = 6, y = 5 - 3x
y = 2x + 4, y = 5 - 3x
y = 5 - 3x, y = - 4
Q5.
Which of the following equations have a solution where both the coordinates are positive?
x - 2y = 6, y = -4
x - 2y = 6, y = 5 - 3x
Correct answer: y = 2x + 4, y = 5 - 3x
y = 5 - 3x, y = - 4