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Given, arc QR is congruent to arc LN and arc OP is congruent to arc VW.
And the expressions for each arc in the diagram also given as:
Arc QR = 2x - y, arc LN = 11 , arc OP= 10 and arc VW=5x+y.
Hence, we will get the system of equations as following:
Arc QR = Arc LN
2x - y = 11 ...(1)
Arc OP = Arc VW
5x + y = 10 ...(2)
Next step is to add the two equation to eliminate y so that we can solve the equations for x. Therefore,
2x+5x = 11 + 10
7x = 21
Divide each sides by 7.
So, x= 3
Now plug in x=3 in equation (2) to get the value of y.
5(3) + y = 10
15 + y =10
15 + y - 15 = 10 - 15 Subtracting 15 from each sides.
y = -5
So, x=3 and y =-5