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Solving Simultaneous Equations Graphically (1)

In this worksheet, students solve simple simultaneous equations graphically by finding the point of intersection on an x-y graph.

'Solving Simultaneous Equations Graphically (1)' worksheet

Key stage:  KS 4

Curriculum topic:  Algebra

Curriculum subtopic:  Recognise, Sketch and Interpret Graphs of Linear/Quadratic/Cubic/Reciprocal Functions

Difficulty level:  

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Worksheet Overview

QUESTION 1 of 10

Simultaneous equations can be solved by drawing the line representing each equation and then finding the point of intersection between the two lines.

Use y = mx + c, or other methods, to draw the lines.

 

Example

By drawing the lines of these equations on a set of coordinate axes, solve the following equations simultaneously:


y = x + 2

x + y = 3

 

Answer

 y = x + 2 has a gradient of 1 and an intercept on the y-axis at (0, 2)

 

x + y = 3 can be rearranged to read 

y = 3 - x which has a gradient of -1 and an intercept on the y-axis at (0, 3)

 

The lines are drawn on a set of coordinate axes

The point of intersection is (½, 2½) and this is the only point at which both equations are satisfied.

So the solution to the simultaneous equations is

x = ½, y = 2½

By drawing the lines of these equations on a set of coordinate axes, solve the following equations simultaneously:


y = x - 2

y = 4 - x

x = 1, y = 2

x = 1, y = 3

x = 3, y = 1

By drawing the lines of these equations on a set of coordinate axes, solve the following equations simultaneously:


y = x - 2

y = 6 - x

x = 4, y = 2

x = 1, y = 3

x = 3, y = 1

By drawing the lines of these equations on a set of coordinate axes, solve the following equations simultaneously:


y = x - 2

y = 2 - x

x = 4, y = 2

x = 0, y = 2

x = 2, y = 0

By drawing the lines of these equations on a set of coordinate axes, solve the following equations simultaneously:


y = x - 2

y = -4 - x

x = -1, y = 3

x = -1, y = -3

x = 3, y = -1

By drawing the lines of these equations on a set of coordinate axes, solve the following equations simultaneously:


y = x - 2

x + y = 0

x = -1, y = 0

x = -1, y = -3

x = 1, y = -1

By drawing the lines of these equations on a set of coordinate axes, solve the following equations simultaneously:


y = x + 6

x + y = 0

x = 3, y = -3

x = -3, y = 3

x = 1, y = -1

By drawing the lines of these equations on a set of coordinate axes, solve the following equations simultaneously:


y = x + 6

x + y = -1

x = -3½, y = 2½

x = -3, y = 3½

x = 3½, y = -2½

By drawing the lines of these equations on a set of coordinate axes, solve the following equations simultaneously:


y = x - 3

x + y = -1

x = 3, y = 0

x = -3, y = -6

x = 1, y = -2

By drawing the lines of these equations on a set of coordinate axes, solve the following equations simultaneously:


y = x - 2

x + y = -3

x = -½, y = -2½

x = -3, y = 2½

x = 2½, y = -½

By drawing the lines of these equations on a set of coordinate axes, solve the following equations simultaneously:


y - x = 5

y + x = 2

x = -1½, y = -3½

x = -3, y = 2½

x = -1½, y = 3½

  • Question 1

By drawing the lines of these equations on a set of coordinate axes, solve the following equations simultaneously:


y = x - 2

y = 4 - x

CORRECT ANSWER
x = 3, y = 1
EDDIE SAYS

The point of intersection is (3, 1).

  • Question 2

By drawing the lines of these equations on a set of coordinate axes, solve the following equations simultaneously:


y = x - 2

y = 6 - x

CORRECT ANSWER
x = 4, y = 2
EDDIE SAYS

The point of intersection is (4, 2).

  • Question 3

By drawing the lines of these equations on a set of coordinate axes, solve the following equations simultaneously:


y = x - 2

y = 2 - x

CORRECT ANSWER
x = 2, y = 0
EDDIE SAYS

The point of intersection is (2, 0).

  • Question 4

By drawing the lines of these equations on a set of coordinate axes, solve the following equations simultaneously:


y = x - 2

y = -4 - x

CORRECT ANSWER
x = -1, y = -3
EDDIE SAYS

The point of intersection is (-1, -3).

  • Question 5

By drawing the lines of these equations on a set of coordinate axes, solve the following equations simultaneously:


y = x - 2

x + y = 0

CORRECT ANSWER
x = 1, y = -1
EDDIE SAYS

The point of intersection is (1, -1).

  • Question 6

By drawing the lines of these equations on a set of coordinate axes, solve the following equations simultaneously:


y = x + 6

x + y = 0

CORRECT ANSWER
x = -3, y = 3
EDDIE SAYS

The point of intersection is (-3, 3).

  • Question 7

By drawing the lines of these equations on a set of coordinate axes, solve the following equations simultaneously:


y = x + 6

x + y = -1

CORRECT ANSWER
x = -3½, y = 2½
EDDIE SAYS

The point of intersection is (-3½, 2½).

  • Question 8

By drawing the lines of these equations on a set of coordinate axes, solve the following equations simultaneously:


y = x - 3

x + y = -1

CORRECT ANSWER
x = 1, y = -2
EDDIE SAYS

The point of intersection is (1, -2).

  • Question 9

By drawing the lines of these equations on a set of coordinate axes, solve the following equations simultaneously:


y = x - 2

x + y = -3

CORRECT ANSWER
x = -½, y = -2½
EDDIE SAYS

The point of intersection is (-½, -2½).

  • Question 10

By drawing the lines of these equations on a set of coordinate axes, solve the following equations simultaneously:


y - x = 5

y + x = 2

CORRECT ANSWER
x = -1½, y = 3½
EDDIE SAYS

The point of intersection is (-1½, 3½).

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