Question

9x+7y=55 , 7x+9y=57 std 10

Answer 1

Hey!!!

Good Afternoon

________

We have

9x + 7y = 55
7x + 9y = 57

You see the pair of Equation is in the form

ax + by = c
bx + ay = d

Thus a = 9 , b = 7 , c = 55 and d = 57

See this is the method you'll not find anywhere else


Thus

$x - y = \frac{c - d}{a - b}$

Thus

$x - y = \frac{55 - 57}{9 - 7}$

Thus x - y = -1-----(1)

Similarly

$x + y = \frac{c + d}{a + b}$

Thus

$x + y = \frac{55 + 57}{9 + 7}$

Thus

x + y = 112/16

=> x + y = 7-----(2)

Add (1) and (2)

=> x + y + x - y = 7 - 1

=> 2x = 6

=> x = 3

Using x in (2)

=> x + y = 7

=> y = 4

Thus x = 3 and y = 4

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Hope this helps ✌️

Answer 2

Heya user☺☺

Using the simple method of elemination , we get

9x+7y=55
+ 7x+9y=57
---------------------
16(x+y) = 112

x+y=7 .........eq1

Now reducing x, we get

9x+7y=55
- 9x+9y=63
-------------------
-2y = -8
y = 4 ..........eq2

Putting value of y in eq1, we get

x= 3


so, x=3 and y=4.

Hope this will help you☺☺