1. Solve linear equations x+y=2 and 2x+3y=4 using Substitution Method
Solution:
`x+y=2`
and `2x+3y=4`
Suppose,
`x+y=2 ->(1)`
and `2x+3y=4 ->(2)`
Taking equation `(1)`, we have
`x+y=2`
`=>x=-y+2 ->(3)`
Putting `x=-y+2` in equation `(2)`, we get
`2x+3y=4`
`2(-y+2)+3y=4`
`=>-2y+4+3y=4`
`=>y+4=4`
`=>y=4-4`
`=>y=0`
`=>y=0 ->(4)`
Now, Putting `y=0` in equation `(3)`, we get
`x=-y+2`
`=>x=-1(0)+2`
`=>x=0+2`
`=>x=2`
`:.x=2" and "y=0`
2. Solve linear equations 2x+7y-11=0 and 3x-y-5=0 using Substitution Method
Solution:
`2x+7y-11=0`
`:.2x+7y=11`
and `3x-y-5=0`
`:.3x-y=5`
Suppose,
`2x+7y=11 ->(1)`
and `3x-y=5 ->(2)`
Taking equation `(2)`, we have
`3x-y=5`
`=>y=3x-5 ->(3)`
Putting `y=3x-5` in equation `(1)`, we get
`2x+7y=11`
`=>2x+7(3x-5)=11`
`=>2x+21x-35=11`
`=>23x-35=11`
`=>23x=11+35`
`=>23x=46`
`=>x=2 ->(4)`
Now, Putting `x=2` in equation `(3)`, we get
`y=3x-5`
`=>y=3(2)-5`
`=>y=6-5`
`=>y=1`
`:.y=1" and "x=2`
3. Solve linear equations 3x-y=3 and 7x+2y=20 using Substitution Method
Solution:
`3x-y=3`
and `7x+2y=20`
Suppose,
`3x-y=3 ->(1)`
and `7x+2y=20 ->(2)`
Taking equation `(1)`, we have
`3x-y=3`
`=>y=3x-3 ->(3)`
Putting `y=3x-3` in equation `(2)`, we get
`7x+2y=20`
`7x+2(3x-3)=20`
`=>7x+6x-6=20`
`=>13x-6=20`
`=>13x=20+6`
`=>13x=26`
`=>x=2 ->(4)`
Now, Putting `x=2` in equation `(3)`, we get
`y=3x-3`
`=>y=3(2)-3`
`=>y=6-3`
`=>y=3`
`:.y=3" and "x=2`
This material is intended as a summary. Use your textbook for detail explanation.
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