Answer:
\(x=4\)
\(y=2\)
Step-by-step explanation:
We have been given two congruent circles. We are asked to find the value of x and y.
We have been given that \(OP\cong VW\). This means \(OP=VW\).
Upon substituting our given values, we will get:
\(3x-y=10...(1)\)
We have been given that \(QR\cong LN\). This means \(QR=LN\).
Upon substituting our given values, we will get:
\(x+y=6...(2)\)
From equation (2), we will get:
\(x=6-y\)
Upon substituting this value in equation (1), we will get:
\(3(6-y)-y=10\)
\(18-3y-y=10\)
\(18-4y=10\)
\(18-18-4y=10-18\)
\(-4y=-8\)
\(\frac{-4y}{-4}=\frac{-8}{-4}\)
\(y=2\)
Therefore, the value of y is 2.
Now, we will substitute \(y=2\) in equation (2) to solve for x.
\(x+2=6\)
\(x+2-2=6-2\)
\(x=4\)
Therefore, the value of x is 4.
