Question

Circles M and K are congruent, QR, is congruent to LN and OP is congruent to VW. Find x and y

Answer 1

Answer:

The value of x and y is 2 and 1 respectively.

Step-by-step explanation:

Given that circles M and K are congruent, QR is congruent to LN and OP is congruent to VW.

QR=y , WV=x-1

PO=y,  LN=2x-3

we have to find the value of x and y

As QR is congruent to LN

$y=2x-3$  →    (1)

OP is congruent to VW

$y=x-1$    →   (2)

From equation (1) and (2), we get

$2x-3=x-1$

$2x-x=3-1$

$x=2$

(2) ⇒ $y=2-1=1$

Hence, the value of x and y is 2 and 1 respectively.

Answer 2

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

$\frac{7x}{7} =\frac{21}{7}$ 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

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