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Question
Solve the following pair of linear equation by the elimination method and the substitution method:
x + y = 5 and 2x – 3y = 4
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Solution
x + y = 5 and 2x – 3y = 4
By elimination method
x + y = 5 ...(i)
2x – 3y = 4 ...(ii)
Multiplying equation (i) by (ii), we get
2x + 2y = 10 ...(iii)
2x – 3y = 4 ...(ii)
Subtracting equation (ii) from equation (iii), we get
5y = 6
y = `6/5`
Putting the value in equation (i), we get
`x = 5 - (6/5) = 19/5`
Hence, `x = 19/5 and y = 6/5`
By substitution method
x + y = 5 ...(i)
Subtracting y both side, we get
x = 5 - y ...(iv)
Putting the value of x in equation (ii) we get
2(5 – y) – 3y = 4
-5y = -6
`y = (-6)/-5`
`y = 6/5`
Putting the value of y in equation (iv) we get
`x = 5 – 6/5`
`x = 19/5`
Hence, `x = 19/5` and `y = 6/5`.
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