1. Solve linear equations 7x-8y=11 and 8x-7y=7 using Addition-Substraction Method

Solution:
`7x-8y=11`

and `8x-7y=7`

`=>7x-8y=11 ->(i)`

`=>8x-7y=7 ->(ii)`

Adding Equation `(i)` and `(ii)`, we get

`=>15x-15y=18`

`=>5x-5y=6 ->(iii)` (On simplifying)

Subtracting Equation `(ii)` from `(i)`, we get

`=>-x-y=4`

`=>x+y=-4 ->(iv)` (On simplifying)

Now solving these equations `(iii)` and `(iv)` using substitution method

Suppose,
`5x-5y=6 ->(1)`

and `x+y=-4 ->(2)`

Taking equation `(2)`, we have

`x+y=-4`

`=>x=-y-4 ->(3)`

Putting `x=-y-4` in equation `(1)`, we get

`5x-5y=6`

`=>5(-y-4)-5y=6`

`=>-5y-20-5y=6`

`=>-10y-20=6`

`=>-10y=6+20`

`=>-10y=26`

`=>y=-13/5 ->(4)`

Now, Putting `y=-13/5` in equation `(3)`, we get

`x=-y-4`

`=>x=-1(-13/5)-4`

`=>x=(13-20)/5`

`=>x=-7/5`

`:.x=-7/5" and "y=-13/5`

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2. Solve linear equations -6x+5y=2 and -5x+6y=9 using Addition-Substraction Method

Solution:
`-6x+5y=2`

`6x-5y=-2`

and `-5x+6y=9`

`5x-6y=-9`

`=>6x-5y=-2 ->(i)`

`=>5x-6y=-9 ->(ii)`

Adding Equation `(i)` and `(ii)`, we get

`=>11x-11y=-11`

`=>x-y=-1 ->(iii)` (On simplifying)

Subtracting Equation `(ii)` from `(i)`, we get

`=>x+y=7`

`=>x+y=7 ->(iv)` (On simplifying)

Now solving these equations `(iii)` and `(iv)` using substitution method

Suppose,
`x-y=-1 ->(1)`

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

Taking equation `(1)`, we have

`x-y=-1`

`=>x=y-1 ->(3)`

Putting `x=y-1` in equation `(2)`, we get

`x+y=7`

`(y-1)+y=7`

`=>y-1+y=7`

`=>2y-1=7`

`=>2y=7+1`

`=>2y=8`

`=>y=4 ->(4)`

Now, Putting `y=4` in equation `(3)`, we get

`x=y-1`

`=>x=4-1`

`=>x=3`

`:.x=3" and "y=4`

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