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I need help rq

what is the x-coordinate of the solution to the following system of equations?

x - 2y = 2
3x + y = 6

a) x= -2
b) x=0
c) x= 2
d) x= 3

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We have the system of equations:

x - 2y = 2

3x + y = 6

From equation 1 we express y.

x - 2y = 2

We pass the addend with the variable x from the left to the right and change the sign.

-2y = 2 - x

We divide both parts of the equation by the multiplier of y.

$$\dfrac{(-1)2y}{-2}=\dfrac{2-x}{-2}$$

$$y=\dfrac{x}{2}-1$$

We put the result y in equation 2.

3x + y = 6

We obtain:

$$3x+\left(\dfrac{x}{2}-1\right)=6$$

$$\dfrac{7x}{2}-1=6$$

We pass the free addend -1 from the left to the right, changing the sign.

$$\dfrac{7x}{2}=1+6$$

$$\dfrac{7x}{2}=2$$

We divide both parts of the equation by the multiplier of x.

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

$$x=2$$

What

$$y=\dfrac{x}{2}-1$$

then

$$y=-1+\dfrac{1}{2}\cdot2$$

$$y=0$$

- y = 0
- x = 2

Therefore, the correct option is C.

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