Someone please explain in the most simple way possible please. (edit: i am using elimination)
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In: 1
Two or more equations.
Same variables.
Same values make each equation work.
If you were to draw the graph of both functions you would find one or more points where they meet (intersect). These values of the variables are the solutions to the equations.
You can also determine them algebraically by a variety of methods.
e.g. you have two equations: y = x + 2 and 2x + y = 8
You can look at the first one and say “well, since y = x + 2 I can replace (substitute) the y in the second equation with x + 2” – i.e. 2x + x + 2 = 8 or 3x + 2 = 8
The purpose of doing this is that you now have an equation with only one unknown (x) rather than two (x and y) so it’s very easy to solve: Subtract 2 from each side to leave the ‘x’ term on its own (3x = 6) and then divide both sides by the coefficient (number in front of the x). Dividing both sides by 3 gives x = 2
Now you know x you can look at the other unknown, y. Again y = x + 2; plug in the 2 that you discovered was the value of x: y = 2 + 2 = 4
So x = 2 and y = 4 are the solutions to that pair of simultaneous equations – and if you drew the two on the same axes the lines would intersect at the point (2,4).
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