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Question
Solve the following simultaneous equations by the substitution method:
0.5x + 0.7y = 0.74
0.3x + 0.5y = 0.5
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Solution
The given equations are
0.5x + 0.7y = 0.74 ....(i)
0.3x + 0.5y = 0.5 ....(ii)
Now, consider equation
0.5x + 0.7y = 0.74
⇒ 0.5x = 0.74 - 0.7y
⇒ x = `(0.74 - 0.7y)/(0.5)` ....(iii)
Substituting the value of x in eqn. (ii), we get
`0.3((0.74 - 0.7y)/(0.5)) + 0.5y` = 0.5
⇒ `(0.222 - 0.21)/(0.5) + 0.5y` = 0.5
⇒ `(0.222 - 0.2y + 0.25)/(0.5)` = 0.5
⇒ 0.222 + 0.04y = 0.25
⇒ 0.04y = 0.028
⇒ y = `(0.028)/(0.04)`
= `(28)/(40)`
= `(7)/(10)`
= 0.7
Putting the value of y in eqn. (iii), we get
x = `(0.74 - 0.7(0.7))/(0.5)`
= `(0.74 - 0.49)/(0.5)`
= `(0.25)/(0.5)`
= `(25)/(50)`
= `(1)/(2)`
= 0.5
Thus, the solution set is (0.5, 0.7).
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