Question

Find the value of k for which following system of linear equation has an infinite number of solution:
5x +2y=k
2(k+1)x+ky=(3k+4)

Answer 1

✨✨✨ANSWER✨✨✨✨

FOR a pair of linear equations

• ax + by + c =0

and

• px+qy+r=0

will have infinitely many solutions if it satisfies the condition

$\frac{a}{p} = \frac{b}{q} = \frac{c}{r}$

• now given....
• 5x +2y-k=0
• 2(k+1)x+ky-(3k+4)=0
• therefore

$\frac{5}{2(k + 1)} = \frac{2}{k} = \frac{ - k}{ - (3k + 4)} \\ \frac{5}{2(k + 1)} = \frac{2}{k} \\ 5k = 4k + 4 \\ k = 4$

• the value of k should be 4