Question

Find the value of 4x+ y =-1
3x+2y=3​

Answer 1

$\purple{\bigstar}\underline{\underline{\textsf{\textbf{ Given \: :}}}}$

• 4x + y = - 1
• 3x + 2y = 3

$\pink{\bigstar}\underline{\underline{\textsf{\textbf{ Solution \: :}}}}$

• 4x + y = -1 ⎯⎯ ⠀(i)
• 3x + 2y = 3 ⎯⎯⠀(ii)

$\begin{gathered} \sf \: Now, \: \: (i) \: \times 3 \implies12x + 3y = - 3 \: ⎯⎯ \: \: (iii) \\ \\ \: \: \: \: \: \: \: \: \: \: \sf \: (ii) \: \times 4 \implies12x + 8 y = 12 \:⎯⎯ \: \: (iv) \\ \\ \\ \\ \sf \: \: (iii) - (iv) \sf \implies \: \: \: - 5y \: \: = \: \: \: - 15 \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \sf \implies \: \: \: 5y \: \: = \: \: \: 15 \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \sf \implies \: \: \: y \: \: = \: \: \: \frac{ 15}{5} = 3 \\ \\ \end{gathered}$

$\sf \: Now, \: \: (i) \: \implies \: 4x + y = - 1 \\ \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \sf \implies4x + 3 = - 1\\ \\ \\ \sf \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \implies4x \: \: \: = - 1 - 3 \\ \\ \\ \: \: \: \: \: \: \sf \implies4x = - 4 \\ \\ \\ \: \: \: \sf \implies x = \frac{ - 4}{4} \\ \\ \\ \sf \implies \: x = - 1$

Therefore,

• x = -1
• y = 4

⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯

$\pink{\bigstar}\underline{\underline{\textsf{\textbf{ Verification \: :}}}}$

Putting values in (i),

$\begin{gathered} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \sf \: ( i)\sf \: 4x + y = - 1 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \sf \implies(4\times - 1 ) + 3= - 1 \\ \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \sf \implies - 4 + 3 = - 1\\ \\ \\ \sf \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \implies - 1 \: \: \: = - 1 \\ \\ \\\end{gathered}$

⠀⠀⠀⠀⠀⠀⠀⠀⠀Hence Verified!!

________________________________________

Putting values in (ii),

$\begin{gathered}\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \sf \: (i i)\sf \: 3x + 2y = 3\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \sf \implies(3 \times - 1) + (2 \times 3) = 3 \\ \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \sf \implies - 3 + 6 = 3\\ \\ \\ \sf \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \implies3 \: \: \: = 3 \\ \\ \\ \end{gathered}$

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀Hence Verified!!

Answer 2

${\huge{\boxed{\underline{\textbf{\textsf{\color{lightpink}{An}{\color{lightblue}{sw}{\color{lightgreen}{er}{\color{lightyellow}{:}}}}}}}}}}$

To Solve:

• Find the value of 4x+ y =-1 ; 3x+2y=3

Solⁿ:

• Solving through Substitution Method
• Find x and y

Eqⁿ 1 : 4x + y = -1

Eqⁿ 2 : 3x + 2y = 3

➪In eqⁿ 1 put value of y as (-1 -4x) :-

4x + y = -1

y = -1 - 4x

★ Substituting value of y in Eqⁿ 2

$3x + 2y = 3 \\ \\ 3x + 2( - 1 - 4x) = 3 \\ \\ 3x - 2 - 8x = 3 \\ \\ - 5x = 3 + 2 \\ \\ - 5x = 5 \\ \\ x = \frac{ 5}{ - 5} \\ \\{ \boxed{ \red{ x = - 1}}}$

★ Substituting value of x in Eqⁿ 2 for finding value of y

$3( - 1) + 2y = 3 \\ \\ - 3 + 2y = 3 \\ \\ 2y = 6 \\ \\ y = \frac{6}{2} \\ \\ { \boxed{ \red{y = 3}}}$

☞︎︎︎ Value of x = -1 ; Value of y = 3

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HOPE IT HELPS :)