Question

Please answer to this question it is very urgent
Question no.13


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Answer 1

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By the way You can do by using infinite solution =
a1/a2 = b1/b2 = c1/c2

Answer 2

Answer:

a = 7 and b = 1.

Step-by-step explanation:

Given system of equation are,

2x - ( a - 4 )y = 2b + 1  and 4x - ( a - 1 )y = 5b - 1

To find: value of a & b when system of equation has infinitely many solution.

Condition for infinitely many solution,

$\frac{a_1}{a_2}=\frac{b_1}{b_2}=\frac{c_1}{c_2}$

here, $a_1=2\,,\,b_1=-(a-4)\,,\,c_1=-(2b+1)\,,\,a_2=4\,,\,b_2=-(a-1)\,and\,c_2=-(5b-1)$

so, we have

$\frac{2}{4}=\frac{-(a-4)}{-(a-1)}=\frac{-(2b+1)}{-(5b-1)}$

Equating first 2 equation we get,

$\frac{2}{4}=\frac{a-4}{a-1}$

$2(a-1)=4(a-4)$

$2a-2=4a-16$

$4a-2a=16-2$

$2a=14$

$a=7$

Now, Equating first and last equation we get,

$\frac{2}{4}=\frac{-(2b+1)}{-(5b-1)}$

$\frac{1}{2}=\frac{2b+1}{5b-1}$

$5b-1=2(2b+1)$

$5b-1=4b+2$

$5b-4b=2+1$

$b=3$

Therefore, a = 7 and b = 1.