Question

Find the solution of equation 3x+4y+7=0 and 5x-7y-2=0

Answer 1

• 3x + 4y + 7 = 0 ....... (1)

• 5x - 7y - 2 = 0 ..........(2)

For solving two linear equations in two variables , there are several methods , one of them has been shown here ( Elimination method ) .

• Equation (1) × 5 ,

= 15x + 20y + 35 = 0 ........ (3)

• Equation (2) × 3 ,

= 15x - 21y - 6 = 0 ......... (4)

Now ,

Equation (3) - Equation (4) ,

= 15x + 20y + 35 - ( 15x - 21y - 6 ) = 0

• 15x - 15x + 20y + 21y + 35 + 6 = 0

• 41y + 41 = 0

• y = -41 / 41 = -1

Put y = -1 , in equation (1) to get value of x ,

=> 3x + 4y + 7 = 0

• 3x + 4(-1) + 7 = 0

• 3x - 4 + 7 = 0

• 3x = -3

• x = -3/3 = -1

THEREFORE , SOLUTION OF EQUATIONS IS ,

x = -1 and y = -1 .

Answer 2

${\huge{\pink{\underline{\underline{Question}}}}}$

Find the solution of equation 3x+4y+7=0 and 5x-7y-2=0

${\huge{\pink{\underline{\underline{Answer}}}}}$

Lets Take ${\green{\overline{\green{\underline{\blue{\boxed{\orange{\mathtt{3x + 4y + 7 = 0}}}}}}}}}$ ───── ( 1 )

And next ${\green{\overline{\green{\underline{\blue{\boxed{\orange{\mathtt{5x - 7y - 2 = 0}}}}}}}}}$ ───── ( 2)

$\mathrm\blue{\:Multiple \:eq(1) \:with \:5 \:and \:eq(2) \:by \:3}$

➪ 5 ( 3x + 4y + 7 ) = 0 ────( from eq (1)

➪15x + 20y + 35= 0 ━━━━━━ ( 3)

➪3 ( 5x - 7y - 2 ) =0 ──── ( from eq (2)

➪ 15x - 21y - 6 = 0 ━━━━━━━ ( 4 )

EQUATE BOTH EQ (3) AND (4)

☞︎︎︎ 15x + 20y + 35

☞︎︎︎ 15x - 21y - 6

(-) ⠀(+) ⠀⠀(+) [ sign change ]

───────────

➪⠀ ⠀41y + 41 = 0

➪ ⠀⠀ ⠀ 41y = - 41

➪ ⠀⠀ ⠀⠀y = $\cancel\frac{- 41}{41}$

➪ y = -1

Now equate y value in equation (1)

3x + 4y + 7 = 0

3x + 4(-1) + 7 = 0

3x - 4 + 7 = 0

3x + 3 = 0

3x = 0 - 3

3x = -3

x = $\cancel\frac{-</em><em>3</em><em>}{</em><em>3</em><em>}$

x = -1

${\green{\overline{\green{\underline{\blue{\boxed{\orange{\mathtt{Value \:of \:x = -1 \:and \:y =-1}}}}}}}}}$