Question

Question 6 For which of the following values of k will this system of equations have no solution? 2x - y = 12 X+ ky = 5 A -0.5 B 0.5 с 2 No value of k meets this constraint.

Answer 1

If a system of linear equations have no solution that means the lines are parallel.

thus, to be parallel line the slope of the equation of line must be equal,

`\begin{gathered} In\text{ general equation of line :} \\ y=m(x-a)+b \\ m\text{ is the slope} \end{gathered}`

Given system of linear equation :

`\begin{gathered} 2x-y=12 \\ x+ky=5 \\ \text{Write each equation in the standard form of line } \\ \text{and get the value of 'm' for each equation} \\ y=2x-12 \\ \text{here m =2} \\ y=-(x)/(k)+(5)/(k) \\ here\text{ m =}(-1)/(k) \\ \text{ since for the parallel lines , m should be equal } \\ equate\text{ both the values of m and solve for k,} \\ (-1)/(k)=2 \\ k=(-1)/(2) \\ k=-0.5 \end{gathered}`

Answer : A -0.5