Is it true to say that the pair of equations 2x – 4y = 5 and –x + 2y = 7 has a unique solution? Justify your
answer.
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Is it true to say that the pair of equations 2x – 4y = 5 and –x + 2y = 7 has a unique solution? Justify your
answer.
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2x - 4y = 5 ⇒ 2x - 4y - 5 = 0
-x + 2y = 7 ⇒ -x + 2y - 7 = 0
for unique solution,
[tex]\frac{a_1}{a_2} \neq \frac{b_1}{b_2}[/tex]
here,
[tex]\frac{a_1}{a_2} = \frac{2}{-1} where, \frac{2}{-1} becomes \frac{-2}{1}[/tex]
[tex]\frac{b_1}{b_2} = \frac{-4}{2} where, \frac{-4}{2} becomes \frac{-2}{1}[/tex]
as in this case,
[tex]\frac{a_1}{a_2} = \frac{b_1}{b_2}[/tex]
so we can say that the solution of the pair of equations is not a unique solution.