The solution of the equations 3x−y+13=2x+y+25=3x+2y+16 given by
A
x=2,y=1
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B
x=1,y=1
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C
x=−1,y=−1
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D
x=1,y=2
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Solution
The correct option is Bx=1,y=1 3x−y+13=2x+y+25=3x+2y+16 Now, 3x−y+13=2x+y+25 15x−5y+5=6x+3y+6 9x−8y=1...(1) 2x+y+25=3x+2y+16 12x+6y+12=15x+10y+5 3x+4y=7...(2) Multiply equation (2) by 2 and add (1) 9x+6x=1+14 15x=15 or x=1
Substitute the value of x in equation (1) 9×1−8y=1 y=1 Thus, x=y=1