Question

Find the solution of the following pair of linear equations, by

using the Elimination method.

2x + 3y = 1

3x – 4y = 10
Please write step by step ​

Answer 1

$\LARGE{\bf{\underline{\underline{Solution:-}}}}$

2x + 3y = 1

3x - 4y = 10

⟹ 3(2x + 3y = 1)

2(3x - 4y = 10)

6x + 9y = 3

- 6x - 8y = 20

___________

0 + 17y = -17

⟹ 17y = -17

⟹ y = $\dfrac{-17}{17}$

⟹ y = - 1

___________

Value of y = -1

Let us find the value of x

2x + 3y = 1

⟹ 2x + 3(-1) = 1

⟹ 2x - 3 = 1

⟹ 2x = 1 + 3

⟹ 2x = 4

⟹ x = $\dfrac{4}{2}$

⟹ x = 2

Value of x = 2

$\small{\bf{\underline{\underline{Verification:-}}}}$

3x - 4y = 10

⟹ 3(2) - 4(-1) = 10

⟹ 6 + 4 = 10

⟹ 10 = 10

$\therefore$ L.H.S = R.H.S

$\LARGE{\bf{\underline{\underline{Answer:-}}}}$

x = 2

y = -1

Answer 2

Answer:

\LARGE{\bf{\underline{\underline{Solution:-}}}}

Solution:−

2x + 3y = 1

3x - 4y = 10

⟹ 3(2x + 3y = 1)

2(3x - 4y = 10)

6x + 9y = 3

- 6x - 8y = 20

___________

0 + 17y = -17

⟹ 17y = -17

⟹ y = \dfrac{-17}{17}

17

−17

⟹ y = - 1

___________

Value of y = -1

Let us find the value of x

2x + 3y = 1

⟹ 2x + 3(-1) = 1

⟹ 2x - 3 = 1

⟹ 2x = 1 + 3

⟹ 2x = 4

⟹ x = \dfrac{4}{2}

2

4

⟹ x = 2

Value of x = 2

\small{\bf{\underline{\underline{Verification:-}}}}

Verification:−

3x - 4y = 10

⟹ 3(2) - 4(-1) = 10

⟹ 6 + 4 = 10

⟹ 10 = 10

\therefore∴ L.H.S = R.H.S

\LARGE{\bf{\underline{\underline{Answer:-}}}}

Answer:−

x = 2

y = -1