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`
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`
This material is intended as a summary. Use your textbook for detail explanation.
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