Question

X+1/2y=2;3x-y=1 how to solve this with elimination method

Answer 1

Step-by-step explanation:

Given -

x + y/2 = 2

3x - y = 1

To Find -

• Value of x and y

By Elimination method :-

[ x + y/2 = 2 ] × 1

[ 3x - y = 1 ] × 1/2

→ x + y/2 = 2

3x/2 - y/2 = 1/2

______________

→ x + 3x/2 = 2 + 1/2

→ 2x + 3x/2 = 4 + 1/2

→ 5x/2 = 5/2

→ x = 1

Now, Substituting the value of x on 3x - y = 1, we get :

→ 3x - y = 1

→ 3(1) - y = 1

→ y = 3 - 1

→ y = 2

Hence,

The value of x is 1 and y is 2

Verification :-

• x + y/2 = 2

→ 1 + 2/2 = 2

→ 1 + 1 = 2

LHS = RHS

And

• 3x - y = 1

→ 3(1) - 2 = 1

→ 3 - 2 = 1

→ 1 = 1

LHS = RHS

Hence,

Verified..

It shows that our answer is absolutely correct.

Answer 2

Given equations

$x+\dfrac{1}{2}y =2$

Multiplying by 2, we get,

$2x+y=4--(1)$

$3x-y=1--(2)$

Solving (1) and (2), we get,

$2x+y=4\\\underline{3x-y=1}\\\underline{\underline{5x=5}}}}\\\implies x = 1$

Substituting x, in equation (1), we get,

$2+y=4\\\implies y = 4-2\\\implies y = 2$

$\boxed{\boxed{\bold{Therefore, \ the \ values \ of \ x \ and \ y \ are \ 1 \ and \ 2 \ respectively}}}}}}}}}$