[tex]\begin{gathered} \text{x }-\frac{7x}{6}-\frac{13z}{6}\text{ = 5} \\ 2x+9y-10z=10 \\ 7x-12y-15z=42 \end{gathered}[/tex]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:
[tex]\begin{gathered} \frac{1}{6}(6x\text{ - 7x - 13z = 30)} \\ =\text{ }\frac{6x}{6}-\frac{7x}{6}-\frac{13z}{6}=\frac{30}{6} \\ =\text{ x }-\frac{7x}{6}-\frac{13z}{6}\text{ = 5} \end{gathered}[/tex]
Since the multiplication is only applied to the 1st equation, the other equations will remain the same.
It becomes:
[tex]\begin{gathered} \text{x }-\frac{7x}{6}-\frac{13z}{6}\text{ = 5} \\ 2x\text{ + 9y - 10z = 10} \\ 7x\text{ - 12y - 15z = 42} \end{gathered}[/tex]
