is it true to say that pair of equations - X + 2 y + 2 is equal to 0 and 1 by 2 x minus 1 by 4 y minus 1 is equal to zero has a unique solution justify your answer
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Given:
- X + 2 y + 2 is equal to 0 and 1 by 2 x minus 1 by 4 y minus 1 is equal to zero.
To find:
Is it true to say that pair of equations has a unique solution justify your answer.
Solution:
From given, we have,
- X + 2 y + 2 is equal to 0
⇒ -x + 2y + 2 = 0
ax + by + c = 0
1 by 2 x minus 1 by 4 y minus 1 is equal to zero
⇒ 1/2 x - 1/4 y - 1 = 0
dx + ey + g = 0
The condition for a pair of equation to have a unique solution is as follows:
a/d ≠ b/e
-1 / (1/2) ≠ 2 / (-1/4)
-2 ≠ -8
2 ≠ 8
Therefore, the given pair of equations have a unique solution.
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