algebra : simultaneous equations
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
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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
Example #2
Example #3
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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.
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.
Why not try out the new GCSE Maths interactive pages?
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video: by elimination example#1
interactive: graphical calculation of roots
