Solve the following pair of linear equations by the substitution method (i) x + y = 14 x – y = 4 (ii) s – t = 3 (s/3) + (t/2) = 6
Solve the following pair of linear equations by the substitution method
(i) x + y = 14
x – y = 4
(ii) s – t = 3
(s/3) + (t/2) = 6
(iii) 3x – y = 3
9x – 3y = 9
(i) Given,
x + y = 14 and x – y = 4 are the two equations.
From 1st equation, we get,
x = 14 – y
Now, substitute the value of x in second equation to get,
(14 – y) – y = 4
14 – 2y = 4
2y = 10
Or y = 5
By the value of y, we can now find the exact value of x;
∵ x = 14 – y
∴ x = 14 – 5
Or x = 9
Hence, x = 9 and y = 5.
(ii) Given,
s – t = 3 and (s/3) + (t/2) = 6 are the two equations.
From 1st equation, we get,
s = 3 + t ___________(1)
Now, substitute the value of s in second equation to get,
(3+t)/3 + (t/2) = 6
⇒ (2(3+t) + 3t )/6 = 6
⇒ (6+2t+3t)/6 = 6
⇒ (6+5t) = 36
⇒ 5t = 30
⇒ t = 6
Now, substitute the value of t in equation (1)
s = 3 + 6 = 9
Therefore, s = 9 and t = 6.
(iii) Given,
3x – y = 3 and 9x – 3y = 9 are the two equations.
From 1st equation, we get,
x = (3+y)/3
Now, substitute the value of x in the given second equation to get,
9(3+y)/3 – 3y = 9
⇒9 +3y -3y = 9
⇒ 9 = 9
Therefore, y has infinite values and since, x = (3+y)/3, so x also has infinite values.
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