Find the value of x and y for the given system of equations : 3x+2y=6,5x+y=2

The correct option is x=-(2/7), y=24/7.

To find the values of $x$ and $y$ that satisfy the given system of linear equations, we can use the method of substitution. Let's write down the given equations:

$$3x+2y=6$$

and

$$5x+y=2$$

First, we can express $y$ in terms of $x$ using the second equation by subtracting $5x$ from both sides:

$$y=2-5x$$

Next, we substitute this expression for $y$ into the first equation:

$$3x+2(2-5x)=6$$

Now, we distribute the $2$ to simplify the equation:

$$3x+4-10x=6$$

Combine the like terms containing $x$:

$$-7x+4=6$$

Subtract $4$ from both sides of the equation to isolate the term with $x$:

$$-7x=6-4$$

$$-7x=2$$

Divide both sides by $-7$ to find $x$:

$$x=-\frac{2}{7}$$

To find the corresponding value of $y$, substitute the value of $x$ back into our expression for $y$:

$$y=2-5\left(-\frac{2}{7}\right)$$

Simplify the multiplication:

$$y=2+\frac{10}{7}$$

Convert $2$ to a fraction with a denominator of $7$ to add the terms:

$$y=\frac{14}{7}+\frac{10}{7}$$

$$y=\frac{24}{7}$$

Thus, the final values are $x=-\frac{2}{7}$ and $y=\frac{24}{7}$.