Question

solving systems of linear equations: medium
google classroom microsoft teams
$y = 0.25x+12$
$y = k(x + 3)$
in the system of equations, $k$ is a constant. for which value of $k$ does the system have no solution?
choose 1 answer:
a 0
b 0.25
c 0.75
d 12

Explanation:

Step1: Recall condition for no - solution

For a system of linear equations $y = m_1x + b_1$ and $y=m_2x + b_2$, if $m_1=m_2$ and $b_1
eq b_2$, the system has no solution. Rewrite the second equation $y = K(x + 3)$ as $y=Kx+3K$. Here, $m_1 = 0.25$, $b_1 = 12$, $m_2=K$, and $b_2 = 3K$.

Step2: Set slopes equal

Set $m_1=m_2$. So we set $K = 0.25$. When $K = 0.25$, the first equation is $y=0.25x + 12$ and the second is $y=0.25x+3\times0.25=0.25x + 0.75$. Since $12
eq0.75$ when $K = 0.25$, the system has no solution.

Answer:

B. $0.25$