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Question
Solve the following simultaneous equations by the substitution method:
7(y + 3) - 2(x + 2) = 14
4(y - 2) + 3(x - 3) = 2
Solution
The given equations are
7(y + 3) - 2(x + 2) = 14 ....(i)
4(y - 2) + 3(x - 3) = 2 ....(ii)
Consider
7(y + 3) - 2(x + 2) = 14
⇒ 7y + 21 - 2x - 4 = 14
⇒ -2x + 7y = -3
⇒ 2x - 7y = 3
⇒ 2x = 7y + 3
⇒ x = `(7y + 3)/(2)` ....(iii)
Now, consider equation
4(y - 2) + 3(x - 3) = 2
⇒ 4y - 8 + 3x - 9 = 2
⇒ 3x + 4y = 19
⇒ `3((7y + 3)/(2)) + 4y` = 19 ....[From (iii)]
⇒ `(21y + 9 + 8y)/(2)` = 19
⇒ 29y + 9 = 38
⇒ 29y = 29
⇒ y = 1
Substituting value of y in eqn. (iii), we get
x = `(7(1) + 3)/(2)`
= `(10)/(2)`
= 5
Thus, the solution set is (5, 1).
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