Problem

$\left\{\begin{array}{l}2 y-7 z=-17 \\ 3 y-11 z=-27\end{array}\right.$

Answer

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Answer

Thus, our answer is \(\boxed{(2,3)}\)

Steps

Step 1 :First, we can find the value of $y$ by multiplying the first equation by $3$ and the second equation by $2$ and then subtracting the first equation from the second equation.

Step 2 :\(6y-21z=-51\)

Step 3 :\(6y-22z=-54\)

Step 4 :Subtracting the first equation from the second equation, we get:

Step 5 :\(z=3\)

Step 6 :Now, we can substitute the value of $z$ into the first equation to find the value of $y$:

Step 7 :\(2y-7(3)=-17\)

Step 8 :\(2y-21=-17\)

Step 9 :\(2y=4\)

Step 10 :\(y=2\)

Step 11 :Thus, our answer is \(\boxed{(2,3)}\)

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