Question

5x + 3y = 9 ……. (i)
2x + 3y = 12 ……… (ii)
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Answer 1

AnsWer :

x = 3. and y = -2.

Given :

We have equation,

• 5x + 3y = 9.
• 2x -3y = 12.

Solution :

We have two equation,

$\tt5x + 3y = 9. - - - (1)$

$\tt2x - 3y = 12. - - - (2)$

Let's apply Elimination method, on both Equation

[tex]\begin{tabular}{ 1-1 } 5x + 3y = 9. & \\ 2x -3y = 12. & \\ \cline{1-1} 7x = 21. & \\ \cline{1-1} \end{tabular}[/tex]

$\implies \tt x = \frac{21}{7}$

$\implies \tt x = 3.$

Now, Putting the value of x in equation (2), We get.

$\implies \tt 2x - 3y = 12.$

$\implies \tt 2(3)- 3y = 12.$

$\implies \tt 6- 3y = 12.$

$\implies \tt - 3y = 12 - 6$

$\implies \tt y = - \frac{12 - 6}{3}$

$\implies \tt y = - 2.$

$\rule{200}3$

Let's Verify :

$\implies \tt5x + 3y = 9.$

$\implies \tt 5(3) + 3( - 2) = 9.$

$\implies \tt 15 - 6 = 9.$

$\implies \tt 9 = 9.$

Therefore, the value of x = 3 and y= -2.

Answer 2

$\huge{ \underline{ \underline{ \green{ \sf{ SoLuTiOn :-}}}}}$

5x + 3y = 9 ---------------(1)

2x - 3y = 12 --------------(2)

By applying the substitution method =>

Equation (1)=>

$5x + 3y = 9 \\ \\ 5x = 9 - 3y \\ \\ x = \frac{9 - 3y}{5} - (3) \\ \\ putting \: x = \frac{9 - 3y}{5} in \: equ. \: (2) \\ \\ 2( \frac{9 - 3y}{5} ) - 3y = 12 \\ \\ \frac{18 - 6y}{5} - 3y = 12$

18 - 6y - 15y = 60

18 - 21y = 60

- 21y = 60 - 18

- 21y = 42

y = - 42/21

y = - 2

then putting the value of y = -2 in equ. (3)=>

$x = \frac{9 - 3y}{5} \\ \\ x = \frac{9 - 3( - 2)}{5} \\ \\ x = \frac{9 + 6}{5} \\ \\ x = \frac{15}{5} \\ \\ x = 3 \: \\ \\ \huge{\blue{\underline{\purple{\mathbb{AnSwER}}}}} \\ \\ {\red{\boxed{\large{\bold{x = 3 \: and \: y = - 2}}}}}$

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