Question

Find the solution for the following pair of equations
$2x+y=8$
$3x-2y=5$

• A. $(2,4)$
• B. $(3,2)$
• C. $(1,-1)$
• D. $(-1,10)$

Answer 1

The correct option is B $(3,2)$

Given pair of equations
$2x+y=8\dots \left(i\right)$
and $3x-2y=5\dots \left(ii\right)$

Step 1: Find the value of x
Multiplying both the sides by $2$ in equation $\left(i\right),$ we get
$\Rightarrow 4x+2y=16$
Now, $2\times \left(i\right)+\left(ii\right)$
$\Rightarrow 4x+2y+3x-2y=16+5\Rightarrow 7x=21$
Dividing both the sides by $7,$ we get
$\Rightarrow x=\frac{21}{7}\Rightarrow x=3$

Step 2: Find the value of y
Putting $x=3$ in $\left(ii\right),$ we get
Equation $\left(ii\right)\to 3\left(x\right)-2y=5$
$\Rightarrow 3\times 3-2y=5\Rightarrow 9-5=2y$
$\Rightarrow 2y=4$
Dividing both the sides by $2,$ we get
$\Rightarrow y=2$
$\therefore x=3,y=2$
$\therefore$ Required solution for the given equations is $(3,2).$