Question

Find the solution for the following pair of equations
$2y+x=4$
$3y-\frac{1}{2}x=2$

• A. $(1,2)$
• B. $(2,1)$
• C. $(0,2)$
• D. $(2,3)$

Answer 1

The correct option is B $(2,1)$

Given,
$2y+x=4\Rightarrow x=4-2y\dots \left(i\right)$
and $3y-\frac{1}{2}x=2\dots \left(ii\right)$

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

Step 2: Now, Find the value of x
Substitute $y=1$ in equation $\left(i\right)$
Equation $\left(i\right)$ $\to$ $x=4-2\left(y\right)$
$x=4-2\left(1\right)$
$\Rightarrow x=4-2=2$
$\therefore x=2,y=1$

$\therefore$ Required solution for the given pair of equations is $(2,1)$