# Representing simultaneous equations graphically (Part 1)

## Lesson details

### Key learning points

1. In this lesson, we will learn how to solve simultaneous equations graphically by plotting them and identifying their point of intersection.

### 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.
What are the equations of the lines in the graph?
y = -4x + 2 and y = x - 1
Correct answer: y = 4x - 2 and y = -x - 1
y = 4x - 2 and y = -x + 1
y = 4x + 2 and y = x - 1
Q2.
Estimate the point of intersection for the lines in the graph.
(-0.2, - 1.2)
(-0.2, 1.2)
(0.2, 1.2)
Q3.
How would you change y = 4x - 2 in order to increase the x-ordinate of the point of intersection?
Decrease the gradient or increase the y-intercept.
Increase the gradient or decrease the y-intercept.
Increase the gradient or the y-intercept.
Q4.
How would you change y = 4x - 2 in order to increase the y-ordinate of the point of intersection?
Decrease the gradient or increase the y-intercept.
Decrease the gradient or the y-intercept.
Increase the gradient or decrease the y-intercept.
Q5.
How would you change y = -x - 1 in order to decrease the x-ordinate of the point of intersection?
Decrease the gradient or increase the y-intercept.
Increase the gradient or decrease the y-intercept.
Increase the gradient or the y-intercept.

## Exit 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