15. Find the values a and b for which the following pair of linear equ

1.	15. Find the values a and b for which the following pair of linear equations have an infinitely number of solutions:(i) ( a + b ) x – 2 b y = 5 a + 2b + 1, 3x – y = 14 (ii) ( 2 a -1 ) x + 3 y = 5 , 3 x + ( b – 1 ) y = 2
Answer» Answer: (i) a = 5 b=1 Step-by-step explanation: Infinite no. of solutions are possible if and only if- $\frac{a_{1} }{a_{2} } = \frac{b_{1} }{b_{2} } =\frac{c_{1} }{c_{2}}$ For (i) $a_{1}$ = (a+b) $b_{1} = -2\\ b_{2} = -1$ $a_{2}$ = 3 and $c_{1}= -5a-2b-1\\c_{2} = -14$ so, $\frac{a_{1}}{a_{2}}$ = (a+b)/3 and $\frac{b_{1}}{b_{2}} =$ -2/-1= 2 Since $\frac{a_{1}}{a_{2}} = \frac{b_{1}}{b_{2}}$ Therefore (a+b)/3 = 2 so, a+b =6.................EQ. (1) ALSO, $\frac{b_{1}}{b_{2}} =\frac{c_{1}}{c_{2}}$ So, 2= (5a + 2b + 1)/14 or 5a + 2b = 27................eq (2) Solving (1) and (2) , we get a = 5 b=1 Similarly you can SOLVE for (ii) Hope this is useful. Please rate the answer!