2.
Note:A different way of saying the above concept is whether the unknowns have the same co-efficients (sign and absolute value).
This leads to 4 cases to be looked at separately.
SAME SIGN DIFFERENT SIGN
SAME NUMBER case 1 case 2
DIFFERENT NUMBER case 3 case 4
General approach to eliminating an unknown.
A.First decide which unknown ( x or y ) you wish to eliminate.
B.Be sure that this unknown has the same co efficient in front of it if necessary by multiplying one or both equations.
C.If the unknowns have the same sign,subtract the equations
D.if the unknowns have different signs add the equations.
Note:Elimination leaves one equation with one unknown,which can be solved to find the unknown which was eliminated ( x or y ).Either unknown can be found.
Case 1.Elimination method with unknowns having the same sign and same co efficient.
X + Y = 5..........1
( co efficients of X are negative and have same number.)
X - Y = 1..........2
We can eliminate the X by subtracting equation 2 from equation 1.Thus, 1. X + Y = 5
2. X - Y = 1 (subtract equation 2 from equation 1) thus
1. X + Y = 5
2. - X - Y = 1
2Y = 4
Note the X term has been eliminated.One equation in one unknown is left which can be solved to find the unknown.This value can then be substituted
into one of the original simultaneous equations using algebra to find the other unknown.
Case 2.Elimination method with different signs and same number.
X + Y = 5...............1
X - Y = 1...............2
1. X + Y = 5
2. +X - Y = 1
2X = 6
We solve for the unknown (X) using substitution method.
SOLVE THIS EQUATION:
2 L + 2 W = 124
L = 5W - 10
SOLVE:
L = 5W - 10 ; 2L + 2W = 124
2(5W - 10) + 2W = 124 .......................Clear parenthesis
12w - 20 = 124 .................................Collect the terms
12w - 20 = 124...................................Simplify by adding like terms (20) to both sides
w = 12 ..........................................Isolate by dividing