When solving simultaneous equations (or systems of equations), several methods can be used such as Cramer's Rule, the substitution method or the elimination method.
Solving For Two Unknowns
The elimination method, involves eliminating one of the variables ("x" or "y") by adding or subtracting the 2 equations.
Example 1:
A) 2x + 3y = 29
B) -2x + 7y = 21
Adding the 2 equations we get:
10y = 50
and so y =5
Putting y = 5 into either equation, we can solve for "x".
Let's use equation A):
A) 2x + 3*5 = 29
A) 2x + 15 = 29
A) 2x = 14
x = 7
We have just used the elimination method to solve for "x" and "y".
However, it is very rare that one variable can be so easily eliminated.
Let's try another example:
Example 2:
A) 4x + 5y = 37
B) 2x - 3y = -9
Adding the 2 equations produces 6x - 2y = 28 which doesn't help us at all.
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