Question

Find the solution for the following pair of equations
$2x+y=2$
$x+2y=5$

• A. $(-\frac{1}{3},\frac{8}{3})$
• B. $(0,\frac{5}{2})$
• C. $(0,2)$
• D. $(1,0)$

Answer 1

The correct option is A $(-\frac{1}{3},\frac{8}{3})$

Given pair of equations
$2x+y=2\dots \left(i\right)$
and $x+2y=5$
$\Rightarrow x=5-2y\dots \left(ii\right)$

Step 1: Find the value of y
Substituting $x=5-2y$ in $\left(i\right),$ we get
Equation $\left(i\right)$ $\to$ $2x+y=2$
$2(5-2y)+y=2$
$\Rightarrow 10-4y+y=2\Rightarrow 10-2=4y-y\Rightarrow 8=3y\Rightarrow y=\frac{8}{3}$

Step 2: Now, Find the value of x
Substitute $y=\frac{8}{3}$ in equation $\left(i\right)$
Equation $\left(ii\right)$ $\to$ $x=5-2y$
$x=5-2\left(\frac{8}{3}\right)$
$\Rightarrow x=5-\frac{16}{3}$
$\Rightarrow x=5\times \frac{3}{3}-\frac{16}{3}$
$\Rightarrow x=\frac{15}{3}-\frac{16}{3}$
$\Rightarrow x=\frac{15-16}{3}$
$\Rightarrow x=\frac{-1}{3}$
$\therefore x=-\frac{1}{3},y=\frac{8}{3}$

$\therefore$ Required solution for the given pair of equations is $(-\frac{1}{3},\frac{8}{3}).$