# Comparing algebraic and graphical methods for solving simultaneous equations

# Comparing algebraic and graphical methods for solving simultaneous equations

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## Lesson details

### Key learning points

- In this lesson, we will learn about the benefits of using graphical or algebraic methods to solve simultaneous equations.

### 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.

Which of the following statements is true?

Simultaneous equations always have solutions.

Simultaneous equations can only be solved using graphs.

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

y = x + 3, y = 2x + 3

Q3.

Which of the following equations have a solution where the x coordinate is negative?

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?

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

y = 5 - 3x, y = - 4

### 5 Questions

Q1.

Which of the following statements is true?

You can only solve simultaneous equations algebraically.

You can only solve simultaneous equations using graphs.

You can solve all simultaneous equations.

Q2.

Which of the following equations can you solve simultaneously?

2y + 4x = 12 and y = -2x + 4

y + 1 = x and y - x = 12

y = 3x + 4 and y - 3x = 12

Q3.

Solve y = 4x - 5 and 2y + 6x = 18 simultaneously using a graphical method.

y = -2, x = 3

y = 2, x = -3

y = 2, x = 3

Q4.

Solve 2y = 6x - 10 and 3y + 6x = 15 simultaneously using an algebraic method.

x = 1, y = 2

x = 2, y = -1

y = 2, x = 3

Q5.

Solve y + x = 5 and y = 5x + 11 simultaneously using both an algebraic method and a graphical method.

x = -6, y= 1

x = 1, y= - 6

x = 6, y = -1