Question

X+2y=3/2 ,2x+y=3/2 by elimination method

Answer 1

Step-by-step explanation:

Given -

x + 2y = 3/2

2x + y = 3/2

To Find -

• Value of x and y

By Elimination method :-

→ [ x + 2y = 3/2 ] × 1

[ 2x + y = 3/2 ] × 2

→ x + 2y = 3/2

4x + 2y = 3

(-) (-) (-)

___________

→ -3x = 3/2 - 3

→ -3x = 3-6/2

→ -3x = -3/2

→ x = 1/2

Now, Substituting the value of x on 2x + y = 3/2 , we get :

→ 2(1/2) + y = 3/2

→ 1 + y = 3/2

→ y = 3/2 - 1

→ y = 3-2/2

→ y = 1/2

Hence,

The value of x is 1/2 and y is 1/2

Verification :-

• x + 2y = 3/2

→ 1/2 + 2×1/2 = 3/2

→ 1/2 + 1 = 3/2

→ 1+2/2 = 3/2

→ 3/2 = 3/2

LHS = RHS

And

• 2x + y = 3/2

→ 2×1/2 + 1/2 = 3/2

→ 1 + 1/2 = 3/2

→ 2+1/2 = 3/2

→ 3/2 = 3/2

LHS = RHS

Hence,

Verified...

Answer 2

$\large{\underline{\bf{\green{Given:-}}}}$

✰ x +2y =3/2

✰ 2x +y = 3/2

$\large{\underline{\bf{\green{To\:Find:-}}}}$

✰ we need to find the Value of x

$\huge{\underline{\bf{\red{Solution:-}}}}$

$\sf\:x +2y =\frac{3}{2}.............(i)$

$\sf 2x +y = \frac{3}{2}.............(ii)$

Multiply equation (i) by 2.

we get,

$\sf2x+4y=3...........(iii)$

from equation (ii) and (iii).

$\sf{\cancel{2x}} + 4y = 3 \\ \sf{\cancel{2x}} + y = \frac{3}{2} \\ - \: \: \: \: \: - \: = \: -$

_______________

y = 1/2

Now

putting value of y in equation (ii)

$\sf 2x +y = \frac{3}{2}.............(ii)$

$:\implies2x+\frac{1}{2}=\frac{3}{2} \\ \\ \sf:\implies \frac{4x + 1}{2} = \frac{3}{2} \\ \\:\implies \sf8x + 2 = 6 \\ \\ :\implies \sf8x = 4\\ \\ :\implies \sf \: x = \frac{4}{8} </p><p>\\=>x=\frac{1}{2}$

So,

$\bf{\pink{x=\frac{1}{2}\:and\:y=\frac{1}{2}}}$

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