Question

Obtain an equivalent system by performing the stated elementary operation on the system. Multiply the first equation by 1/66x7y132 = 302x +102 = 10 12y7x15z = 42-16x7y132 = 30Z2X +102 =10+-N11gy12y7x15z =42-y -=(Type integers or simplified fractions)

Answer 1

`\begin{gathered} \text{x }-(7x)/(6)-(13z)/(6)\text{ = 5} \\ 2x+9y-10z=10 \\ 7x-12y-15z=42 \end{gathered}`Step-by-step explanation:

6x - 7y - 13z = 30 ...equation 1

2x + 9y - 10z = 10 ...equation 2

7x - 12y - 15z = 42 ...equation 3

Multiply the 1st equation by 1/6:

`\begin{gathered} (1)/(6)(6x\text{ - 7x - 13z = 30)} \\ =\text{ }(6x)/(6)-(7x)/(6)-(13z)/(6)=(30)/(6) \\ =\text{ x }-(7x)/(6)-(13z)/(6)\text{ = 5} \end{gathered}`

Since the multiplication is only applied to the 1st equation, the other equations will remain the same.

It becomes:

`\begin{gathered} \text{x }-(7x)/(6)-(13z)/(6)\text{ = 5} \\ 2x\text{ + 9y - 10z = 10} \\ 7x\text{ - 12y - 15z = 42} \end{gathered}`