3x+2y=7;4x-y=2 solve by substittution and elimination mrthod

1.	3x+2y=7;4x-y=2 solve by substittution and elimination mrthod
Answer» align="ABSMIDDLE" alt="\sf{\red{\huge{\boxed{\bold{ Substitution \: METHOD}}}}}" class="latex-formula" id="TexFormula1" src="https://tex.z-dn.net/?F=%5Csf%7B%5Cred%7B%5Chuge%7B%5Cboxed%7B%5Cbold%7B%20Substitution%20%5C%3A%20method%7D%7D%7D%7D%7D" title="\sf{\red{\huge{\boxed{\bold{ Substitution \: method}}}}}"> ⠀⠀ $\sf{\bold{\green{\underline{\underline{Given}}}}}$ 3x + 2y = 7 4x - y = 2 ______________________ $\sf{\bold{\green{\underline{\underline{To\:Find}}}}}$ find x and y ______________________ $\sf{\bold{\green{\underline{\underline{Solution}}}}}$ ⠀⠀⠀⠀ 4x - y = 2 ⠀⠀⠀⠀ 4x - 2 = y ⠀⠀⠀⠀ y = 4x - 2 ---- ( i ) ⠀⠀⠀⠀ 3x + 2y = 7 ⠀⠀⠀⠀ putting value of x from eq ( i ) ⠀⠀⠀⠀ 3x + 2 ( 4x - 2 ) = 7 ⠀⠀ 3x + 8x - 4 = 7 ⠀⠀⠀⠀ 11x - 4 = 7 ⠀⠀⠀⠀ 11x = 7 + 4 ⠀⠀⠀⠀ 11x = 11 ⠀⠀⠀⠀ x = 11 / 11 ⠀⠀⠀⠀ x = 1 ⠀⠀⠀⠀ putting value of x in eq ( i ) ⠀⠀⠀⠀ y = 4 × 1 - 2 ⠀⠀⠀⠀ y = 4 - 2 ⠀⠀ y = 2 ______________________ $\sf{\bold{\green{\underline{\underline{Answer}}}}}$ value of X = 1 Value of y = 2 ⠀⠀⠀⠀ $\sf{\red{\huge{\boxed{\bold{ Eliminating \: method}}}}}$ ⠀⠀⠀⠀ $\sf{\bold{\green{\underline{\underline{Given}}}}}$ 3x + 2y = 7 4x - y = 2 ______________________ $\sf{\bold{\green{\underline{\underline{To\:Find}}}}}$ Value of x and y ______________________ $\sf{\bold{\green{\underline{\underline{Solution}}}}}$ ⠀⠀⠀⠀ 3x + 2y = 7 ---- ( i ) ⠀⠀⠀⠀ 4x - y = 2 ---- ( ii ) ⠀⠀⠀⠀ Multiply eq ( ii ) by 2 ⠀⠀⠀⠀ 8x - 2y = 4 ---- ( iii ) ⠀⠀⠀⠀ Adding eq i and ii ⠀⠀⠀⠀ 3x + 2y + 8x - 2y = 7 + 4 ⠀⠀⠀⠀ 3x + 8x = 7 + 4 ⠀⠀⠀⠀ 11x = 7 + 4 ⠀⠀⠀⠀ 11x = 11 ⠀⠀⠀⠀ x = 11 / 11 ⠀⠀⠀⠀ x = 1 ⠀⠀⠀⠀ putting value of x in eq ( i ) ⠀⠀⠀⠀ 3x + 2y = 7 ⠀⠀ 3 × 1 + 2y = 7 ⠀⠀⠀⠀ 3 + 2y = 7 ⠀⠀⠀⠀ 2y = 7 - 3 ⠀⠀⠀⠀ 2y = 4 ⠀⠀⠀⠀ y = 4 / 2 ⠀⠀⠀⠀ y = 2 ______________________ $\sf{\bold{\green{\underline{\underline{Answer}}}}}$ value of x = 1 value of y = 2

Answer»

align="ABSMIDDLE" alt="\sf{\red{\huge{\boxed{\bold{ Substitution \: METHOD}}}}}" class="latex-formula" id="TexFormula1" src="https://tex.z-dn.net/?F=%5Csf%7B%5Cred%7B%5Chuge%7B%5Cboxed%7B%5Cbold%7B%20Substitution%20%5C%3A%20method%7D%7D%7D%7D%7D" title="\sf{\red{\huge{\boxed{\bold{ Substitution \: method}}}}}">

⠀⠀

$\sf{\bold{\green{\underline{\underline{Given}}}}}$

3x + 2y = 7
4x - y = 2

______________________

$\sf{\bold{\green{\underline{\underline{To\:Find}}}}}$

find x and y

______________________

$\sf{\bold{\green{\underline{\underline{Solution}}}}}$

⠀⠀⠀⠀

4x - y = 2

⠀⠀⠀⠀

4x - 2 = y

⠀⠀⠀⠀

y = 4x - 2 ---- ( i )

⠀⠀⠀⠀

3x + 2y = 7

⠀⠀⠀⠀

putting value of x from eq ( i )

⠀⠀⠀⠀

3x + 2 ( 4x - 2 ) = 7

⠀⠀

3x + 8x - 4 = 7

⠀⠀⠀⠀

11x - 4 = 7

⠀⠀⠀⠀

11x = 7 + 4

⠀⠀⠀⠀

11x = 11

⠀⠀⠀⠀

x = 11 / 11

⠀⠀⠀⠀

x = 1

⠀⠀⠀⠀

putting value of x in eq ( i )

⠀⠀⠀⠀

y = 4 × 1 - 2

⠀⠀⠀⠀

y = 4 - 2

⠀⠀

y = 2

______________________

$\sf{\bold{\green{\underline{\underline{Answer}}}}}$

value of X = 1
Value of y = 2

⠀⠀⠀⠀

$\sf{\red{\huge{\boxed{\bold{ Eliminating \: method}}}}}$

⠀⠀⠀⠀

$\sf{\bold{\green{\underline{\underline{Given}}}}}$

3x + 2y = 7
4x - y = 2

______________________

$\sf{\bold{\green{\underline{\underline{To\:Find}}}}}$

Value of x and y

______________________

$\sf{\bold{\green{\underline{\underline{Solution}}}}}$

⠀⠀⠀⠀

3x + 2y = 7 ---- ( i )

⠀⠀⠀⠀

4x - y = 2 ---- ( ii )

⠀⠀⠀⠀

Multiply eq ( ii ) by 2

⠀⠀⠀⠀

8x - 2y = 4 ---- ( iii )

⠀⠀⠀⠀

Adding eq i and ii

⠀⠀⠀⠀

3x + 2y + 8x - 2y = 7 + 4

⠀⠀⠀⠀

3x + 8x = 7 + 4

⠀⠀⠀⠀

11x = 7 + 4

⠀⠀⠀⠀

11x = 11

⠀⠀⠀⠀

x = 11 / 11

⠀⠀⠀⠀

x = 1

⠀⠀⠀⠀

putting value of x in eq ( i )

⠀⠀⠀⠀

3x + 2y = 7

⠀⠀

3 × 1 + 2y = 7

⠀⠀⠀⠀

3 + 2y = 7

⠀⠀⠀⠀

2y = 7 - 3

⠀⠀⠀⠀

2y = 4

⠀⠀⠀⠀

y = 4 / 2

⠀⠀⠀⠀

y = 2

______________________

$\sf{\bold{\green{\underline{\underline{Answer}}}}}$

value of x = 1
value of y = 2