Lesson 14. Simultaneous equations on a graph

EXAMPLE:

If x = 2 and y = 8 then 4x + y = 16

If x = 3 and y = 4 then 4x + y = 16

There are many pants of values of x and y which fit the equation

4x + y = 16

There are also many pairs of values of x and y which fit the equation

15x – y = 3

There is only one pair of values of x and y which satisfy both equations at the same time (simultaneously).

The 2 equations are called simultaneous equations.

x = 1 and y = 12 are called the solutions of the simultaneous equations.

The solutions of simultaneous equations can be found by drawing a graph.

EXAMPLE:

Solve the simultaneous equations

3x + y = 6   x + y = 4

(a) Draw the line 3x + y = 6

      when x = 0, y = 6

      when y = 0, 3x = 6 so x = 2

(b) Draw the line x + y = 4

      when x = 0, y = 4

      when y = 0,  x = 4

(c) The lines intersect at (1, 3).

      The solutions of these simultaneous equations are

      x = 1, y = 3. 

Lesson 14

•  Test 1