Question

which ordered pair is a solution to the system of linear equations 1/2 x - 3/4 y = 11/60 and 2/5 x + 1/6 y = 3/10?

Answer 1

Value of $x=\frac{2}{3}\,\,and\,\,value\,\,of\,\,y=\frac{1}{5}$

Solution set is  $(\frac{2}{3},\frac{1}{5})$

Step-by-step explanation:

We need to solve the following system of equations:

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

We can solve this using Substitution.

Isolate x in $\frac{1}{2}x-\frac{3}{4}y=\frac{11}{60}$

$\frac{1}{2}x=\frac{11}{60}+\frac{3}{4}y\\ x=\frac{11}{30}+\frac{3}{2}y$

Putting value of x in equation(2)

$\frac{2}{5}(\frac{11}{30}+\frac{3}{2}y)+\frac{1}{6}y=\frac{3}{10}\\Solving:\\Taking\,\,LCM\,\,of\,\,5,6,10 \,\,we\,\,get: 30\\Multiply\,\,by\,\,LCM\\\frac{2}{5}(\frac{11}{30}+\frac{3}{2}y)\times30+\frac{1}{6}y\times30=\frac{3}{10}\times30\\Simplifying:\\12(\frac{11}{30}+\frac{3}{2}y)+5y=9\\\frac{22}{5}+18y+5y=9\\23y=9-\frac{22}{5}\\23y=\frac{45-22}{5}\\23y=\frac{23}{5}\\y=\frac{\frac{23}{5} }{23}\\y=\frac{1}{5}$

Putting value of y=1/5 in $x=\frac{11}{30}+\frac{3}{2}y$

$x=\frac{11}{30}+\frac{3}{2}\times\frac{1}{5} \\x=\frac{11}{30}+\frac{3}{10}\\x=\frac{11+3*3}{30}\\x=\frac{11+9}{30} \\x=\frac{20}{30}\\x=\frac{2}{3}$

So, value of $x=\frac{2}{3}\,\,and\,\,value\,\,of\,\,y=\frac{1}{5}$

Solution set is  $(\frac{2}{3},\frac{1}{5})$

Keywords: System of linear Equations

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