Question

For what value of k will the following pair of linear equations have infinitely many solutions?
2x − 3y = 7, (k + 1)x + (1 − 2k)y= 5k− 4

Answer 1

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# NIKKY

Answer 2

Answer:

Step-by-step explanation:

The given equations are:

2x − 3y = 7 and

(k + 1)x + (1 − 2k)y= 5k− 4

It is given that the given pair of linear equations have infinitely many solutions, therefore

$\frac{a_{1}}{a_{2}}=\frac{b_{1}}{b_{2}}=\frac{c_{1}}{c_{2}}$

Here, $a_{1}=2$, $b_{1}=-3$, $c_{1}=-7$, $a_{2}=(k+1)$, $b_{2}=(1-2k)$ and $c_{2}=-(5k-4)$

Now, $\frac{2}{k+1}=\frac{-3}{11-2k}=\frac{-7}{-(5k-4)}$

Taking first and second equality, we get

$2-4k=-3k-3$

$-4k+3k=-3-2$

$-k=-5$

$k=5$

Thus, the value of k is 5.