Answer:
[tex]x=4[/tex]
[tex]y=2[/tex]
Step-by-step explanation:
We have been given an image of two congruent circles. We are asked to find the value of x and y for our given circles.
Since [tex]\overline{QR}\cong\overline{LN}[/tex], so [tex]\overline{QR}=\overline{LN}[/tex].
[tex]x+y=6...(1)[/tex]
Since [tex]\overline{OP}\cong\overline{VW}[/tex], so [tex]\overline{OP}=\overline{VW}[/tex].
[tex]3x-y=10...(2)[/tex]
From equation (1), we will get:
[tex]x=6-y[/tex]
Upon substituting this value in equation (2), we will get:
[tex]3(6-y)-y=10[/tex]
Upon using distributive property, we will get:
[tex]18-3y-y=10[/tex]
[tex]18-4y=10[/tex]
[tex]18-18-4y=10-18[/tex]
[tex]-4y=-8[/tex]
[tex]\frac{-4y}{-4}=\frac{-8}{-4}[/tex]
[tex]y=2[/tex]
Therefore, the value of y is 2.
Now, we will substitute [tex]y=2[/tex] in equation (1) as:
[tex]x+2=6[/tex]
[tex]x+2-2=6-2[/tex]
[tex]x=4[/tex]
Therefore, the value of x is 4.
