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प्रश्न
Solve the following systems of equations:
`2/sqrtx + 3/sqrty = 2`
`4/sqrtx - 9/sqrty = -1`
उत्तर
`2/sqrtx + 3/sqrty` = 2
`4/sqrtx - 9/sqrty` = –1
Let `1/sqrtx` = p and `1/sqrty` = q
The given equations reduce to:
2p + 3q = 2 ....(1)
4p – 9q = –1 ....(2)
Multiplying equation (1) by (3), we obtain:
6p + 9q = 6 ....(3)
Adding equation (2) and (3), we obtain:
10p = 5
p = `1/2`
Putting the value of p in equation (1), we obtain:
`2 xx 1/2 + 3q = 2`
3q = 1
q = `1/3`
∴ p = `1/sqrtx = 1/2`
`sqrtx` = 2
x = 4
q = `1/sqrty = 1/3`
`sqrty` = 3
y = 9
∴ x = 4, y = 9
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