Find the value of k for which the following pair of linear equations has infinitely many solutions. We have, `2x + 3y = 7 ⇒ 2x + 3y - 7 = 0` For infinitely many solutions `a_1/a_2 = b_1/b_2 = c_1/c_2` ⇒ `(2)/(k+1) = (3)/((2k -1)) = (-7)/-(4k +1)` ⇒ `(2)/(k+1) = (3)/(2k -1)` ⇒ `2(2k + 1) = 3 (k+1)` ⇒`4k - 2 = 3k + 3` ⇒`4k - 3k = 3 +2` `k = 5` or ⇒ `(2)/(k+1) = (-7)/-(4k +1)` ⇒ `2(4k + 1) = 7 (k+1)` ⇒ `8k + 2 = 7k + 2` ⇒`8k - 7k = 7- 2` `k = 5` Hence, the value of k is 5 for which given equations have infinitely many solutions. Concept: Pair of Linear Equations in Two Variables Is there an error in this question or solution?
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This video is only available for Teachoo black users Solve all your doubts with Teachoo Black (new monthly pack available now!) Text Solution Solution : as we know that `a_1x+b_1y+c_1 = 0` <br> `a_2x+b_2y+c_2=0` <br> has infinity solutions only when <br> `a_1/a_2 = b_1/b_2 = c_1/c_2` <br> so here, `k/12= 3/k = -(k-3)/(-k)` <br> `k/12= 3/k` <br> `k^2 = 36` <br> `k= +-6` <br> case 1 : `6/12=3/6=-(6-3)/(-6)` <br> `1/2=1/2=1/2` <br> case 2: `k=-6` <br> `-6/12=3/-6=-(-6-3)/-(-6)` <br> `-1/2=-1/2 = -(-9)/(-(-6)=3/2` <br> `=-1/2=-1/2=3/2` false statement<br> `:.` k = 6 answer Open in App Suggest Corrections 6 |