Sunday, March 31, 2013

Solve the following pair of linear equations by the substitution and cross-multiplication methods: 8x +5y =9 …(1) 3x +2y =4 …(2)

Solve the following pair of linear equations by the substitution and cross-multiplication methods:
8x +5y =9       …(1)
 3x +2y =4      …(2)

 Substitution method :-
8x +5y =9
Subtract 8x both sides we get
5y  = 9 – 8x
Divide by 5

Y = (9 – 8 x)/5 …(3)
Plug this value of y in equation second we get
3x +2y =4
3x  + 2(9 – 8 x)/5) = 4
Multiply by 5 we get
15 x  + 18  - 16 x  = 20
-x  = 2
X = - 2
Plug this value back in equation (3) we get 
Y = (9- 8(-2))/5
Y = 25/5
Y = 5
Answer is x  = -2 and y = 5
Cross multiplication method
8x +5y =9       …(1)
Subtract 9 both side we get
8x +5y – 9 = 0
 3x +2y =4      …(2)
Subtract 4 both side we get
3x + 2y – 4 = 0
Compare with
            we get 
a1 = 8 ,           b1 = 5  ,         and     c1 = -9 
a2  = 3 ,          b2  = 2            and     c2 = -4

Use the formula of cross multiplication



We get
X  = -2   and y = 5

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