Question

simultaneous equations 2x+3y=7;3x-y=5​

Answer 1

Given equations are —

• 2x + 3y =7 ---------------(1)
• 3x - y = 5 -----------------(2)

{ ∆ We will solve it by Substituting Method }

From eq (1) ,

→ 2x = 7 - 3y

→ x = $\bold{\frac{7 - 3y }{2}\:\:--------(3)}$

Putting the value of x in eq(2) we get,

$\implies \: 3 \times \frac{7 - 3y}{2} + 3y = 7$

$\implies \: \frac{21 - 9y}{2} + 3y = 7$

$\implies \: \frac{21 - 9y - 6y}{2} = 7$

$\implies \: {21 - 15y} = 14$

$\implies \: {15y} = 21 - 14$

$\implies \: \underline{\bold { {y} = \frac{7}{15} }}$

Now, Putting the value of y in eq(3) we get ,

$\large \: \: \: \: \bold{x = \frac{7 - 3 \times \frac{7}{15} }{2}}$

$\large \: \: \: \: \bold{ \implies \: x= \frac{7 - \frac{7}{5} }{2}}$

$\large \: \: \: \: \bold{ \implies \: x = \frac{\frac{35 - 7}{5} }{2}}$

$\large \: \: \: \: \bold{ \implies \: x = \frac{\frac{28}{5} }{2}}$

$\large \: \: \: \: \bold{ \implies \: x = \frac{28}{5} \times \frac{1}{2} }$

$\large \: \: \: \: \underline\bold{ \implies \: x = \frac{14}{5} }$

Hence,

★ x = 14/5

★ y = 7/15