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)*(1)/(6) \\ (6x)/(6)-(7y)/(6)-(13z)/(6)=(30)/(6) \\ \implies x-1(1)/(6)y-2(1)/(6)z=5\cdots(4) \end{gathered}`

Therefore, the equivalent system of equations is:

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