Question

Solve by substitution: 3x-y=4 and 4y=3x+11

Answer 1

Step-by-step explanation:

3x-y = 4

y= 3x-4

put above value of y in second equation

4y = 3x + 11

4(3x-4) = 3x + 11

12x - 16 = 3x + 11

12x - 3x = 11 + 16

9x = 27

x = 3

y= 3x - 4

y = 3(3) - 4

y= 9-4

y=5

Answer 2

Answer:-

$\large\leadsto\boxed{\sf\purple{x = 3}}$

$\large\leadsto\boxed{\sf\purple{y = 5}}$

• Given:-

✧ $\sf{3x-y = 4} \: \: \: \longrightarrow\bf\green{[eqn.1]}$

✧ $\sf{4y = 3x + 11} \: \: \: \longrightarrow\bf\green{[eqn.2]}$

• Method:-

✧ Substitution method

• Solution:-

Taking [eqn.1]:-

✧ $\sf{3x-y = 4}$

→ $\bf{y = 3x-4}$

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

✧ $\sf{4y = 3x + 11}$

→ $\sf{4(3x-4) = 3x + 11}$

→ $\sf{12x - 16 = 3x + 11}$

→ $\sf{12x - 3x = 11 + 16}$

→ $\sf{9x = 27}$

→ $\sf{x = \dfrac{27}{9}}$

$\implies\bf\red{x = 3}$

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

✧ $\sf{3x - y = 4}$

→ $\sf{3(3) - y = 4}$

→ $\sf{9 - y = 4}$

→ $\sf{y = 9 - 4}$

$\implies\bf\red{y = 5}$

Hence,

$\pink{\bigstar}$$\large\boxed{\sf{x = 3}}$

$\pink{\bigstar}$$\large\boxed{\sf{y = 5}}$