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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

 

simultaneous #1

 

Example #2

 

simultaneous eq. #2

 

Example #3

 

simultaneous eq. #3

 

 

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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

 

simultaneous 4

 

Example #2

 

simultaneous #5

 

Example #3

 

simultaneous #6

 

 

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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.

 

 

by graph #1

 

 

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.

 

 

simultaneous eq. #2

 

 

 

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