Question

lf 8x-7y=11 and 7x-8y=4,then what is the value of x+y=?​

Answer 1

$\sf{Solution}$

Step by step explanation :-

Given :-

8x - 7y = 11

7x - 8y = 4

To find :-

x + y

Solution:-

8x - 7y = 11 ----- 1

7x - 8y = 4 ------2

Subtracting eq 1 - eq 2

8x - 7y - ( 7x - 8y ) = 11 - 4

8x - 7y - 7x + 8y = 7

Keep like terms together

8x - 7x - 7y + 8y = 7

x + y = 7

So, the value of x + y is 7

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Verification :-

We have to verify that x + y is 7

Take the two equations

8x - 7y = 11

7x - 8y = 4

Adding two equations

8x - 7y + ( 7x - 8y ) = 11 + 4

8x - 7y + 7x - 8y = 15

15x - 15y = 15

Take common 15

15 ( x -y ) = 15

x - y = 1 ----- a

x + y = 7------- b

Adding two equations

x - y + x + y = 1 + 7

2x = 8

x = 8/2

x = 4

Substitute value of x in equation a

x - y = 1

4 - y = 1

4 - 1 = y

y = 3

x = 4

We have to verify x + y

x + y = 3 + 4

x + y = 7

Verified !