Question

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

Answer 1

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

⠀⠀

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

• 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