Coursework Notes - Algebra

Simultaneous Equations

 solution by substitution by elimination using graphs

By substitution

The method is to re-arrange one of the equations in the form 'x =' or 'y =' and substitute the value of x or y into the second equation.

Example #1

Example #2

Example #3

By elimination

Here one equation is altered to make one term in each equation the same(disregarding the +/- sign). These terms are then added or subtracted to eliminate them.

Example #1

Example #2

Example #3

Using graphs

For two separate functions, first write tables for x & y. Then draw the graphs. Where the graph lines intersect is the point that satisfies both equations. Simply read off the x and y values at the point.

The reader may wish to verify the result by one of the other methods given above.

Example

By a graphical method find the coodinates of a point that satisfies the equations x + y = 5 and y - 2x = -2 .

First draw your table, rearranging each equation to make 'y' the subject.

 x 1 2 3 y=5-x 4 3 2 y=2x-2 0 2 4

Then plot the coordinates for each function, drawing straight lines through points.

Where the lines cross gives the solution (2.3,2.7) One decimal place is usually sufficient.

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