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Question
Solve the following simultaneous equations by the substitution method:
0.4x + 0.3y = 1.7
0.7x - 0.2y = 0.8
Solution
The given equations are
0.4x + 0.3y = 1.7 ....(i)
0.7x - 0.2y = 0.8 ....(ii)
Multiplying both the equations by 10, we get
4x + 3y = 17 ....(iii)
7x - 2y = 8 ....(iv)
Now, consider equation
4x + 3y = 17
⇒ 4x = 17 - 3y
⇒ x = `(17 - 3y)/(4)` ....(v)
Substituting the value of x in eqn. (iv), we get
`7((17 - 3y)/(4)) - 2y` = 8
⇒ `(119 - 21y)/(4) - 2y` = 8
⇒ `(119 - 21y - 8y)/(4)` = 8
⇒ 119 - 29y = 32
⇒ -29y = 32 - 119
⇒ -29y = -87
⇒ y = `(-87)/(-29)`
= 3
Putting the value of y in eqn. (v), we get
x = `(17 - 3(3))/(4)`
= `(17 - 9)/(4)`
= `(8)/(4)`
= 2
Thus, the solution set is (2, 3).
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