Let's solve the equation step by step to find the values of [tex]\( x \)[/tex] and [tex]\( y \)[/tex].
1. Simplify the given fraction [tex]\(\frac{-14}{63}\)[/tex]:
We can simplify [tex]\(\frac{-14}{63}\)[/tex] by dividing both the numerator and the denominator by their greatest common divisor (GCD), which is 7.
[tex]\[
\frac{-14}{63} = \frac{-14 \div 7}{63 \div 7} = \frac{-2}{9}
\][/tex]
2. Now, let's equate [tex]\(\frac{x}{9}\)[/tex] to the simplified fraction [tex]\(\frac{-2}{9}\)[/tex]. From this equality:
[tex]\[
\frac{x}{9} = \frac{-2}{9}
\][/tex]
Since the denominators are the same, we can set the numerators equal to each other:
[tex]\[
x = -2
\][/tex]
3. Next, we equate [tex]\(\frac{-18}{y}\)[/tex] to the simplified fraction [tex]\(\frac{-2}{9}\)[/tex]. From this equality:
[tex]\[
\frac{-18}{y} = \frac{-2}{9}
\][/tex]
To solve for [tex]\( y \)[/tex], we can cross-multiply:
[tex]\[
-18 \cdot 9 = -2 \cdot y
\][/tex]
Simplifying this, we get:
[tex]\[
-162 = -2y
\][/tex]
Dividing both sides by [tex]\(-2\)[/tex]:
[tex]\[
y = \frac{-162}{-2} = 81
\][/tex]
Therefore, the values of [tex]\( x \)[/tex] and [tex]\( y \)[/tex] are:
[tex]\[
(x, y) = (-2, 81)
\][/tex]
