Answer:
[tex]\{\frac{2}{3}, \frac{1}{5}\}[/tex]
ordered pair is the Solution to the given System.
Step-by-step explanation:
Given:
[tex]\frac{1}{2}x- \frac{3}{4}y= \frac{11}{60} ...........Equation( 1 )\\ \\\frac{2}{5}x+ \frac{1}{6}y= \frac{3}{10} ...........Equation( 2 )\\[/tex]
To Check:
Which ordered pair is the Solution to the given System. ?
Solution:
If [tex]\{\frac{2}{3}, \frac{1}{5}\}[/tex]
is the Solution then it must satisfy the given equation. i.e .Left Hand Side (L.H.S) must be Equal to Right Hand Side (R.H.S) of both the given equation for
[tex]\{x=\frac{2}{3}, y=\frac{1}{5}\}[/tex]
∴ For Equation ( 1 )
[tex]L.H.S=\frac{1}{2}\times \frac{2}{3}- \frac{3}{4}\times \frac{1}{5}\\\\\\=\frac{1}{3} -\frac{3}{20} \\\\=\frac{20-9}{20\times 3}\\\\ =\frac{11}{60} \\= R.H.S[/tex]
∴ Left Hand Side = Right Hand Side
Hence,
[tex]\{x=\frac{2}{3}, y=\frac{1}{5}\}[/tex]
The solution.
∴ For Equation ( 2 )
[tex]L.H.S=\frac{2}{5}\times \frac{2}{3}+ \frac{1}{6}\times \frac{1}{5}\\\\\\=\frac{4}{15} -\frac{1}{30} \\\\=\frac{120+15}{15\times 30}\\\\= \frac{135}{450}\\ \\\\=\frac{3}{30}\\ \\= R.H.S[/tex]
∴ Left Hand Side = Right Hand Side
Hence ,
[tex]\{x=\frac{2}{3}, y=\frac{1}{5}\}[/tex]
The solution.
For other Solutions we do not have Left Hand Side equal to Right Hand Side.
i.e Left Hand Side ≠ Right Hand Side
Hence Not a Solution.
