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Question

Solve the following pair of simultaneous equations:
3x+1y=13;2yx=5

A
25 and 4
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B
3 and 14
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C
7 and 17
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D
3 and 34
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Solution

The correct option is C 3 and 14
The equation 3x+1y=13 can be solved as:

3x+1y=133xy+1y=133xy+1=13y.........(1)

The equation 2yx=5 can be solved as:

2yx=52xyy=52xy=5y.........(2)

Multiply the equation 2 by 3. Then we get:

3xy+6=15y.........(3)

Add equations 1 and 3 to eliminate xy, because the coefficients of xy are opposite. So, we get

(3xy3xy)+(1+6)=13y+15y

i.e. 28y=7

i.e. y=14

Substituting this value of y in the equation 1, we get

3x(14)+1=13(14)34x+1=13434x=134134x=943x=9x=3

Hence, the solution of the equations is x=3,y=14.

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