SOLUTION: Use the elimination method to solve the given system of equations. Please show all work. x + 2y = 8; 4x � 5y = 6

Question 864302: Use the elimination method to solve the given system of equations. Please show all work.
x + 2y = 8;
4x � 5y = 6
Answer by DrBeeee(684) (Show Source): You can put this solution on YOUR website!
Use elimination to solve
(1) 4x - 5y = 6 and
(2) x + 2y = 8
To eliminate one of the variables requires that we make the coefficient of that variable equal in both (or all) equations. In this case we can do it by multiplying (2) by 4, and get
(3) 4x + 8y = 32
Now subtract (1) from (3) and get
(4) 4x - 4x + 8y - (-5y) = 32 - 6 or
(5) 13y = 26 or
(6) y = 2
Note that x is eliminated by the subtraction in (4), thus the "elimination" method.
Now use (2) to find x
(7) x + 2*2 = 8 or
(8) x = 8 - 4 or
(9) x = 4
Chech this solution pair using (1).
Is (4*4 - 5*2 = 6)?
Is (16 - 10 = 6)?
Is (6 = 6)? Yes
Answer: The solution pair is (4,2).
Comment: The reason I stated to make the coefficient equal for ALL equations is that many systems have many more than two equations and the elimination method is, in general, use on high speed computers to solve for the solution set (more than a pair) in real time. Especially on aircraft control systems.
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