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If $3 x + 7 y = − 1$ and $4 y − 5 x + 14 = 0,$ and then find the values of $3 x − 8 y and y x − 2$ then find the values of .

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The value of

3 x − 8 y

is 5 and

y x − 2

− 5 2

The value of

3 x − 8 y

is 14 and

y x − 2

− 5 2

The value of

3 x − 8 y

is 9 and

y x − 2

− 5 2

The value of

3 x − 8 y

is 11 and

y x − 2

− 5 2

answer is B.

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Detailed Solution

Given equations are

3 x + 7 y = − 1

and

4 y − 5 x + 14 = 0.

Let the given equations be,

3 x + 7 y = − 1

……………(1)

4 y − 5 x = − 14

………..(2)
Multiply equation (1) with 5.

15 x + 35 y = − 5

................(3)
Multiplying equation (2) by 3.

− 15 x + 12 y = − 42

........……(4)
Adding equation (3) and (4).

15 x + 35 y + − 15 x + 12 y = − 5 + − 42

15 x + 35 y − 15 x + 12 y = − 5 − 42

35 y + 12 y = − 5 − 42

47 y = − 47

y = − 1

Put y= -1 in equation (1).

3 x + 7 − 1 = − 1

3 x − 7 = − 1

3 x = 6

x = 63

x = 2

Now, find the value of

3 x − 8 y

3 x − 8 y = 32 − 8 − 1

3 x − 4 y = 6 + 8

3 x − 4 y = 14

Now, find the value of

y x − 2

y x − 2 = − 1 2 − 2

y x − 2 = − 1 2 − 2 × 22

y x − 2 = − 1 2 − 42

y x − 2 = − 5 2

Hence, the value of

3 x − 8 y

is 14 and

y x − 2

− 5 2

.
The correct option is (2).

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If 3x+7y=−1 and 4y−5x+14=0, and then find the values of 3x−8y and y x −2 then find the values of .

Start JEE / NEET / Foundation preparation at rupees 99/day !!

Detailed Solution

Get Expert Academic Guidance – Connect with a Counselor Today!

If $3 x + 7 y = − 1$ and $4 y − 5 x + 14 = 0,$ and then find the values of $3 x − 8 y and y x − 2$ then find the values of .