in figure,l|m, then find the value of x
Answers
According to the question :-
14 = 3y + x
↦ 3y + x = 14 ( equation 1)
20 = 2y - 3x
↦- 3x + 2y = 20 ( equation 2 )
Now, we will multiply equation 1 from 3,
we will get,
\begin{gathered}\leadsto \sf \: 3(3y + x) = 3 \times 14 \: \: \: \: \: \: \: \: \: \: \: \: \\ \leadsto \sf \: 9y + 3x = 42 \: ( equation \: 3)\end{gathered}⇝3(3y+x)=3×14⇝9y+3x=42(equation3)
On adding equation 2 and 3, we get,
\begin{gathered}\dashrightarrow \sf9y + 2y + 3x - 3x = 42 + 20 \\ \dashrightarrow \sf11y = 62 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \dashrightarrow \sf \: y = \frac{62}{11} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \end{gathered}⇢9y+2y+3x−3x=42+20⇢11y=62⇢y=1162
Now, since we have obtained the value of y, we can easily find out the value of x by Substituting the value of y in equation 1,
So, after Substituting the value of y i.e. 62/11 in equation 1, we have,
\begin{gathered}\dashrightarrow \sf3y + x = 14 \: \: \: \: \: \: \\\dashrightarrow \sf3( \frac{62}{11} ) + x = 14 \\ \dashrightarrow \sf \frac{186}{11} + x = 11 \: \: \: \\ \dashrightarrow \sf3y + x = 14 \: \: \: \: \: \: \\\dashrightarrow \sf3( \frac{62}{11} ) + x = 14 \\ \dashrightarrow \sf \: x = 14 - \frac{186}{11} \: \: \\ \dashrightarrow \sf \: x = \frac{154 - 186}{11} \\\dashrightarrow \sf \: x = \frac{ - 32}{11} \: \: \: \: \: \: \: \: \: \: \: \end{gathered}⇢3y+x=14⇢3(1162)+x=14⇢11186+x=11⇢3y+x=14⇢3(1162)+x=14⇢x=14−11186⇢x=11154−186⇢x=11−32
\begin{gathered} \sf \pink{\therefore x = \frac{ - 32}{11} } \\ \sf \orange{ y = \frac{62}{11}} \: \: \: \: \: \: \: \end{gathered}∴x=11−32y=1162
NOTE :- For verification you can put the values of x and y in equation 1 and check whether L.H.S. = R.H.S.
If they are equal, then they would be verified.