Question

Solve the linear equation by elimination method.

x + y = 5 and 2x - 3y = 4
Plz help me I will give you 5 points.

Answer 1

Solution :

$\bf{\red{\underline{\bf{Given\::}}}}$

x + y = 5 & 2x - 3y = 4

$\bf{\red{\underline{\bf{To\:find\::}}}}$

The value of x and y.

$\bf{\red{\underline{\bf{Explanation\::}}}}$

We have;

$\bullet\sf{x+y=5....................(1)}\\\bullet\sf{2x-3y=4...................(2)}$

We can multiplying equation (1) by 2 :

$\longrightarrow\sf{2(x+y)=2\times 5}\\\\\longrightarrow\sf{2x+2y=10...........................(3)}$

Now, subtracting equation (3) from equation (2),we get;

$\begin{aligned} \sf{2x-3y & = 4} \\ \sf{2x+2y & =10}\\ (-)\:\:(-)&\:\:\:\:(-) \\ \cline{1-2}\sf{ -5y& =-6\\ \cline{1-2}\end{aligned}}$

$\longrightarrow\sf{\cancel{-}5y=\cancel{-}6}\\\\\longrightarrow\sf{5y=6}\\\\\longrightarrow\sf{\pink{y=\dfrac{6}{5} }}$

Putting the value of y in equation (1), we get;

$\longrightarrow\sf{x+\bigg(\dfrac{6}{5} \bigg)=5}\\\\\\\longrightarrow\sf{5x+6=25}\\\\\\\longrightarrow\sf{5x=25-6}\\\\\\\longrightarrow\sf{5x=19}\\\\\\\longrightarrow\sf{\pink{x=\dfrac{19}{5} }}$

Thus;

The value of x is 19/5 and y is 6/5 .

Answer 2

Aɴꜱᴡᴇʀ

☞ $\green{ \rm x = \large \frac{6}{5} }$

☞ $\rm \purple{y = \frac{19}{5} }$

_________________

Gɪᴠᴇɴ

✭ x + y = 5 ................... 1

✭ 2x - 3y = 4 ..................... 2

_________________

ᴛᴏ ꜰɪɴᴅ

➠ The values of X and Y

_________________

Sᴛᴇᴘꜱ

Elimination method is a very simple method. We know how to solve an equation in one variable, so in this method also we eliminate a variable and make it a variable in one variable.

So here let's eliminate x ( We can also eliminate Y, we are just eliminating X here )

$\large \orange{\underline{\sf{}Multiplying \:Equation \: (1) \: by \: 2}}\\ \\ \tt\leadsto{}2(x + y) = 2(5) \\ \\ \tt \leadsto{}2x + 2y = 10 \: ........ \: 3 \\ \\ \large \orange {\underline{\sf{}Now \: Subtracting \: Equation \:2 \: by \: 3 }} \\ \\ \tt \hookrightarrow( \cancel{2x} - 3y = 4) - ( \cancel{2x} + 2y = 10) \\ \\ \tt \hookrightarrow (- 5y )= ( - 6) \\ \\ \tt \red{ \hookrightarrow \red{y = \frac{6}{5} }}$

➜ So now we found the value of y and so let's find the value of X by substituting the value of y in equation....1

$\tt \dashrightarrow{}x + y = 5 \\ \\ \tt \dashrightarrow{}x = 5 - y \\ \\ \tt \dashrightarrow{}x = 5 - \frac{6}{5} \\ \\ \tt \dashrightarrow{}x = \frac{25 - 6}{5} \\ \\ \tt \pink{ \dashrightarrow{}x = \frac{19}{5} }$

__________________________________