Question

Find the value of k for the following equations having infinitely many solutions
3x – (k + 1)y = 20 and (k + 2)x – 10y = 40. ​

Answer 1

Hope this answer helped you....Thank u!

Answer 2

Answer:

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=>Condition for infinitely many Solutions-

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

=>$\frac{3}{k+2}$=$\frac{k+1}{10}$=$\frac{20}{40}$

1.On taking first and second -

=>$\frac{3}{k+2}$=$\frac{k+1}{10}$

=>$30=(k+1)(k+2)$

=>$30=k^2+3k+2$

=>$k^2+3k-28=0$

=>$k^2+7k-4k-28=0$

=>$k(k+7)-4(k+7)=0$

=>$(k-4)(k+7)=0$

K=4 and K=-7

2.Now taking second and third-

=>$\frac{k+1}{10}$=$\frac{20}{40}$

=>$\frac{k+1}{10}$=$\frac{1}{2}$

=>$2k+2=10$

=>K=$\frac{8}{2}$

=>$K=4$

Since K=4 is common in both solutions-

$\huge\orange{\fbox{\pink{\text{K=4}}}}$

$\huge{\purple{\bigstar{\blue{\text{Hope it helps...}}}}}$