Question

solve for the system of linear equation by substitution method 3x-2y=7and 4x+3y=12​

Answer 1

3x=7+2y

x=7+2y/3

putting the value in 2nd eq

4(7+2y/3)+3y=12

28+8y/3+3y=12

28+8y+9y/3=12

28+17y=36

17y=36-28

y=8/17

putting this value in eq 1

x=7+2*8/3*17

x=7+16/51

x=357+16/51

x=373/51

the valus are 373/51and 8/17

Answer 2

Answer:-

$\red{\bigstar}$ $\large\leadsto\boxed{\sf{\purple{x = \dfrac{45}{17}}}}$

$\red{\bigstar}$ $\large\leadsto\boxed{\sf{\purple{y = \dfrac{8}{17}}}}$

• Given:-

$\sf{3x-2y = 7} \longrightarrow\bf{[eqn.1]}$

$\sf{4x + 3y = 12} \longrightarrow\bf{[eqn.2]}$

• Method:-

Substitution method

• Solution:-

Taking eqn.[1]:-

$\bf{3x-2y = 7}$

→ $\sf{3x = 7+2y}$

→ $\sf\pink{x = \dfrac{7+2y}{3}}$

• Substituting the value of x in eqn.[2]:-

$\bf{4x+3y=12}$

→ $\sf{4 \bigg(\dfrac{7+2y}{3}\bigg) +3y = 12}$

→ $\sf{\dfrac{28+8y}{3} +3y = 12}$

→ $\sf{\dfrac{28+8y+9y}{3} = 12}$

→ $\sf{28+8y+9y = 12 \times 3}$

→ $\sf{28+ 17y = 36}$

→ $\sf{17y = 36 - 28}$

→ $\sf\red{y = \dfrac{8}{17}}$

Now,

• Substituting the value of y in eqn.[1]:-

$\bf{3x-2y = 7}$

→ $\sf{3x - 2 \bigg(\dfrac{8}{17} \bigg) = 7}$

→ $\sf{3x - \dfrac{16}{17} = 7}$

→ $\sf{3x = 7 + \dfrac{16}{17}}$

→ $\sf{3x = \dfrac{119 + 16}{17}}$

→ $\sf{3x = \dfrac{135}{17}}$

→ $\sf{x = \dfrac{135}{17 \times 3}}$

→ $\sf{x = \dfrac{135}{51}}$

→ $\sf\red{x = \dfrac{45}{17}}$