Question 89045: i. Explain how to apply elimination in solving a system of equations.
ii. Explain how to apply substitution in solving a system of equations.
iii. Demonstrate each technique in solving the system
1. 3x + 9y = 12
2. 5x - 4y = 3
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i. Explain how to apply elimination in solving a system of equations.
ii. Explain how to apply substitution in solving a system of equations.
iii. Demonstrate each technique in solving the system
To solve a system of linear equation by elimination process
1)Bring the co-efficient of any one variable to the same .
2) If the signs of both variable are same (having the same co-efficients)
then subtract the two eq's.
3)If the signs are different then add the two eq'ns so that like terms get eliminated.
4)The value of one variable is calculated
5)By subtituting the value of known variable unknown variable can be
found.
solution: 1. 3x + 9y = 12
2. 5x - 4y = 3
1)L.C.M of 3,5 = 15 hence bring the co-efficient of x to 15
multiply eq'n(1) by 5 , and eq'n(2) by 3. The two eq'ns
reduces to 15x+45y = 60
15x-12y = 9
2) subtract the two eq'ns we get 57y = 51 , y = 51/57
3) substituting the value of y in eq'n (1) we get
3x+9(51/57) = 12
3x = 12- (459/57) = 684-459/57 = 225/57
x = 225/57*3 = 75/57
solution is x = 75/57 and y = 51/57
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