Question

$-33y=6(3z+3)-39y$, $6y-22=c(z-3)$
For what value of $c$ does the above system of linear equations in the variables $y$ and $z$ have infinitely many solutions?

• A. 5/7
• B. 17/15
• C. 7/11
• D. 11/2

Answer 1

The correct option is D 11/2

Let's rewrite the equation
$\begin{array}{c}-33y=18z+18-33y\\ 6y-18z=18\end{array}|\begin{array}{c}6y-22=cz-3c\\ 6y-cz=22-3c\end{array}$
$6y-18z=18$
$6y-cz=22-3c$
If the ratio of x coeff = ratio of coeff = ratio of constant coeff
Therefore,
$\frac{-18}{-c}=\frac{18}{22-3c}$
$\frac{18}{c}=\frac{18}{22-3c}$
$22-3c=c$
$22=4c$
$c=\frac{22}{4}=\frac{11}{2}$