Circles M and K are congruent, arc QR is congruent to arc LN and arc OP is congruent to arc VW. Find x.
1 answer:
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)
We need to find the value of x. So, we can add the equations 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
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Answer:
B. equivalent
Step-by-step explanation:
Our two equations are:
Let's use substitution and plug in the expression for y in the second equation. That way, we're getting rid of a variable so we can solve for the other:
This means that there are an infinite number of solutions possible for this system - any x value will work. So, the answer is equivalent, because these two equations are essentially the same.