Question

For what value of (k) the equation have a unique
2x+3y=1,kx+5y=7​

Answer 1

Step-by-step explanation:

solution:-

the given system of equation is

2x+3y-1=0,kx +5y-7=0

this is of the form of :- a1x+b1y+c1=0,a2x+b2y+c2=0

where a1=2 ,b1=3 ,c1=-1 and a2=k,b2=5 ,c2=-7

for a unique solution , we must have

$\frac{a1}{a2} \not = \: \frac{b1}{b2} \\ \implies \frac{2}{k} \not = \frac{3}{5} \\ \implies \: k \not = \frac{10}{3}$

hence the given system of equation will have a unique solution when

$k \not = \frac{10}{3}$