Question

If 2x + 3y = 10 and 2x + y = 15, find the value of (x + y).​

Answer 1

Step-by-step explanation:

from the attachment above we got the values X and Y

that is :

• x = 35/4
• y = -5/2

according to the question,

$x + y = \frac{35}{4} - \frac{5}{2}$

$x + y = \frac{35 - 10}{4}$

$x + y = \frac{25}{4}$

Answer 2

Step-by-step explanation:

Given : Two linear equations $2x+3y=10$  and  $2x+y=15$ .

To find : The value of $(x+y)$.

• Calculation for x and y

To find the $(x+y)$ we have to find the values of x and y first. As we have linear equations

⇒  $2x+3y=10$               --(1)

⇒  $2x+y=15$                 --(2)

so we can find the $x$ and $y$ by substitution method.

Extract $x$ from equation (1),

⇒  $x=\frac{10-3y}{2}$                   --(3)

Substitute this $x$ in equation (2),

⇒ $2x+y=15$  

⇒ $2(\frac{10-3y}{2})+y=15$

⇒ $10-3y+y=15$

taking similar terms at one side,

⇒ $-3y+y=15-10$

⇒ $-2y=5$

⇒ $y=\frac{-5}{2}$

now put this y in equation (3)

⇒  $x=\frac{10-3y}{2}$    

        $=\frac{10-3(\frac{-5}{2})}{2}$

        $=\frac{10+(\frac{15}{2})}{2}$

taking L.C.M of 2 in numerator of  $x$.

         $=\frac{(\frac{20+15}{2})}{2}$

         $=\frac{\frac{35}{2}}{2}$

         $=\frac{35}{4}$

We get the values of x and y as

$x=\frac{35}{4}$    and  $y=\frac{-5}{2}$.

• Calculation for $(x+y)$

We have ,

$x=\frac{35}{4}$    and  $y=\frac{-5}{2}$.

So the $(x+y)$ is,

⇒  $x+y=\frac{35}{4} +(\frac{-5}{2})$

              $=\frac{35}{4} -\frac{5}{2}$

taking L.C.M as 4,

              $=\frac{35-10}{4}$

              $=\frac{25}{4}$

Hence we get the value of $(x+y) =\frac{25}{4}$ .