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प्रश्न
Solve the following systems of equations:
0.5x + 0.7y = 0.74
0.3x + 0.5y = 0.5
उत्तर
The given systems of equations is
0.5x + 0.7y = 0.74 .....(i)
0.3x + 0.5y = 0.5 ....(ii)
Multiplying (i) and (ii) by 100, we get
50x + 70y = 74 .....(iii)
30x + 50y = 50 ....(iv)
From (iii), we get
50x = 74 - 70y
`=> x = (74 - 70y)/50`
Substituting `x = (74 - 70y)/50 ` in equation (iv), we get
`30((74 - 70y)/50) + 50y = 50`
`=> (3(74 - 70y))/y + 50y = 50`
`=> (222 - 210)/5 + 50y = 50`
`=> 222 - 210y + 250y = 250`
=> 40y = 250 - 222
=> 40y= 28
`=> y = 28/40 = 14/20 = 7/10 = 0.7`
Putting y = 0.7 in x = `(74 - 70y)/50` we get
`x = (74 - 70 xx 0.7)/50`
`= (74 - 49)/50`
`= 25/50`
= 1/2
= 0.5
Hence, solution of the given system of equation is x = 0.5, y = 0.7
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