# Representing simultaneous equations graphically (Part 1)

# Representing simultaneous equations graphically (Part 1)

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## Lesson details

### Key learning points

- 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.

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### 5 Questions

Q1.

What are the equations of the lines in the graph?

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.

### 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

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

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

x = 2, y = -5

x = 2, y = 5