Solve: x+2y=3/2 and 2x+y=3
Elimination Method
x+2y=$\frac{3}{2}$
⇒ 2(x+2y) =3
⇒ 2x+4y=3 —(i)
2x+y=3 —-(ii)
Subtracting Equation (ii) from (i) we get,
(2x+4y) -(2x+y)=3-3
⇒ 2x+4y -2x – y = 0
⇒ 3y = 0
⇒ y = $\frac{0}{3}$
⇒ y = 0
From Euqation (ii)
2x+0=3
⇒ 2x = 3
⇒ x = $\frac{3}{2}$
Required Solutions are x = $\frac{3}{2}$ and y = 0
Substitution Method
x+2y=$\frac{3}{2}$
⇒ 2(x+2y) =3
⇒ 2x+4y=3 —(i)
2x+y=3 —-(ii)
From equation (i) we get,
⇒ 2x = 3-4y
⇒ x = $\frac{3 – 4y}{2}$ —(iii)
Substituting the value of x in equation (ii) we get,
$2\left(\frac{3 – 4y}{2}\right) + 4y = 3$
$\Rightarrow 3 – 4y + 4y = 3$
$\Rightarrow 3 – 8y = 3$
$\Rightarrow 3 – 3 = 8y$
$\Rightarrow 8y = 0$
$\Rightarrow y = \frac{0}{8}$
$\Rightarrow y = 0$
From equation (iii) we get,
$x = \frac{3 – 4y}{2}$
$\Rightarrow x = \frac{3 – 4.0}{2}$
$\Rightarrow x = \frac{3}{2}$
Required Solutions are x = $\frac{3}{2}$ and y = 0