Question

Which ordered pair is a solution of linear equations?

Answer 1

Answer:

$\{\frac{2}{3}, \frac{1}{5}\}$

ordered pair is the Solution to the given System.

Step-by-step explanation:

Given:

$\frac{1}{2}x- \frac{3}{4}y= \frac{11}{60} ...........Equation( 1 )\\ \\\frac{2}{5}x+ \frac{1}{6}y= \frac{3}{10} ...........Equation( 2 )$

To Check:

Which ordered pair is the Solution to the given System. ?

Solution:

If  $\{\frac{2}{3}, \frac{1}{5}\}$

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

$\{x=\frac{2}{3}, y=\frac{1}{5}\}$

∴ For Equation ( 1 )

$L.H.S=\frac{1}{2}\times \frac{2}{3}- \frac{3}{4}\times \frac{1}{5}\\\\\\=\frac{1}{3} -\frac{3}{20} \\\\=\frac{20-9}{20\times 3}\\\\ =\frac{11}{60} \\= R.H.S$

∴ Left Hand Side = Right Hand Side

Hence,

$\{x=\frac{2}{3}, y=\frac{1}{5}\}$

The solution.

∴ For Equation ( 2 )

$L.H.S=\frac{2}{5}\times \frac{2}{3}+ \frac{1}{6}\times \frac{1}{5}\\\\\\=\frac{4}{15} -\frac{1}{30} \\\\=\frac{120+15}{15\times 30}\\\\= \frac{135}{450}\\ \\\\=\frac{3}{30}\\ \\= R.H.S$

∴ Left Hand Side = Right Hand Side

Hence ,

$\{x=\frac{2}{3}, y=\frac{1}{5}\}$

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.