Question

Obtain an equivalent system by performing the stated elementary operation on the system. Multiply the first equation by1/6(Type integers or simplified fractions.)

Answer 1

Given the system of equations:

$\begin{gathered} 6x-7y-13z=30\cdots(1) \\ 2x+9y-10z=10\cdots(2) \\ 7x-12y-15z=42\cdots(3) \end{gathered}$

Multiply the first equation by 1/6.

$\begin{gathered} (6x-7y-13z=30)\times\frac{1}{6} \\ \frac{6x}{6}-\frac{7y}{6}-\frac{13z}{6}=\frac{30}{6} \\ \implies x-1\frac{1}{6}y-2\frac{1}{6}z=5\cdots(4) \end{gathered}$

Therefore, the equivalent system of equations is:

$\begin{gathered} x-1\frac{1}{6}y-2\frac{1}{6}z=5\cdots(4) \\ 2x+9y-10z=10\cdots(2) \\ 7x-12y-15z=42\cdots(3) \end{gathered}$