Question

2x-3y=1 3x-4y =1 solve by elimination method

Answer 1

Answer:-

$\pink{\bigstar}$$\large\boxed{\rm\purple{x = \dfrac{7}{17}}}$

$\pink{\bigstar}$$\large\boxed{\rm\purple{y = \dfrac{-1}{17}}}$

• Given:-

✧ $\sf{2x - 3y = 1}\dashrightarrow\bf\red{[eqn.i]}$

✧ $\sf{3x - 4y = 1}\dashrightarrow\bf\red{[eqn.ii]}$

• To Find:-

Value of x and y.

• Method:-

✧ $\sf{Elimination \: Method}$

• Solution:-

Firstly,

Multiplying eqn[i] by 4 and eqn.[ii] by 3:-

• $\sf{4(2x - 3y = 1)}$

→ $\sf{8x - 12y = 4}\dashrightarrow\bf\red{[eqn.iii]}$

• $\sf{3(3x - 4y = 1)}$

→ $\sf{9x - 12y = 3}\dashrightarrow\bf\red{[eqn.iv]}$

Adding eqn.[iii] and eqn.[iv]:-

→ $\sf{8x - 12y + (9x - 12y) = 4 + 3}$

→ $\sf{8x - 12y + 9x - 12y = 7}$

→ $\sf{8x + 9x = 7}$

→ $\sf{17x = 7}$

→ $\large\bf\green{x = \dfrac{7}{17}}$

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

• $\sf{2x - 3y = 1}$

→ $\sf{2 \times \dfrac{7}{17} - 3y = 1}$

→ $\sf{\dfrac{14}{17} - 3y = 1}$

→ $\sf{\dfrac{14}{17} - 1 = 3y }$

→ $\sf{\dfrac{14-17}{17} = 3y}$

→ $\sf{\dfrac{-3}{17} = 3y }$

→ $\sf{y = \dfrac{-3}{17 \times 3}}$

→ $\large\bf\green{y = \dfrac{-1}{17}}$