Question

solve the following pairs of equation by reducing them to a pair 1) 1/2x + 1/3y = 3 and 1/3x + 1/2y = 13/6​

Answer 1

Answer:

x=5/28 and y=5/3

Step-by-step explanation:

Let 1/x=a and 1/y=b

1/2x+1/3y=3

or a/2+b/3=3

Multiplying by 6

6a/2+6b/3=6*3

3a+2b=18----------------------(1)

and

a/3+b/2=13/6

Multiplying by 6

6a/3+6b/2=13*6/6

2a+3b=13------------------------(2)

Multiplying (1() by 3 and (2) by 2

9a+6b=54------------------------(3)

4a+6b=26------------------------(4)

subtracting (4) from(3)

5a=28,a=28/5

Hence a=28/5

or 1/x=28/5  So x=5/28

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putting value of a in (2)

2*28/5+3b=13

56/5+3b=13

3b=13-56/5

3b=65-56/5=9/5

b=3/5

or 1/y=3/5

y=5/3

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So x=5/28 and y=5/3