Answer to Question #230380 in Algebra for moe

Question

You are given the system of linear equations

$2x+ky=5, \quad x+3y=7,$

where k is a constant.

The system above has no solution when k= _________________

Answer 1

The given system of linear equations is:

$2x+ky=5\\x+3y=7$

The given system is of the type:

$a_1x+b_1y+c_1=0,\space a_2x+b_2y+c_2=0$

which has no solution if:

$\frac{a_1}{a_2}=\frac{b_1}{b_2}≠\frac{c_1}{c_2}$

Therefore, the given system can be written as:

$2x+ky−5=0\\x+3y−7=0$

which has no solution if:

$\frac{2}{1}=\frac{k}{3}≠\frac{−5}{−7}\\⇒\frac{2}{1}=\frac{k}{3}⇒\\k=6$

so, the given system has no solution for k=6.