Question

For what values of k is the set of equations 2x - 3(2k - 1)y = 10 and 3x + 4(k + 1)y = 20 are
consistent?​

Answer 1

Answer:

k ∈ R - { 1/26 }

Step-by-step explanation:

Conditions for pair of linear equations

$a_{1}$x + $b_{1}$y = $c_{1}$

$a_{2}$x + $b_{2}$y = $c_{2}$

are consistent with unique solution if

$a_{1}$ / $a_{2}$ ≠ $b_{1}$ / $b_{2}$

are consistent with infinitely many solutions

$a_{1}$ / $a_{2}$ = $b_{1}$ / $b_{2}$ = $c_{1}$ / $c_{2}$

~~~~~~~~~~~~

$\frac{2}{3}$ ≠ $\frac{10}{20}$

Thus, pair of linear equations are consistent with unique solution if

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

- 9(2k - 1) ≠ 8(k + 1)

- 18k + 9 ≠ 8k + 8

26k ≠ 1  

k ≠ $\frac{1}{26}$ ===> all real numbers except 1/26