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प्रश्न
Solve the following simultaneous equation.
x - 2y = -1 ; 2x - y = 7
उत्तर
x - 2y = -1 ...(I)
2x - y = 7 ...(II)
Multiply (I) with 2,
2x - 4y = -2 ....(III)
Subtracting (III) from (II)
2x - y = 7
2x - 4y = -2
- + +
3y = 9
∴ y = 3
Putting the value of y in (I) we get,
∴ x - 2y = -1
⇒ x - 2 × 3 = -1
⇒ x - 6 = -1
⇒ x = -1 + 6
⇒ x = 5
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The ratio of two numbers is 2:3. If 5 is added in each numbers, then the ratio becomes 5:7 find the numbers.
The ratio of two numbers is 2:3.
So, let the first number be 2x and the second number be `square`.
From the given condition,
`((2x) + square)/(square + square) = square/square`
`square (2x + square) = square (square + square)`
`square + square = square + square`
`square - square = square - square`
`- square = - square`
x = `square`
So, The first number = `2 xx square = square`
and, Second number = `3 xx square = square`
Hence, the two numbers are `square` and `square`
