The x - coordinate of the solution is ![x=-2](https://tex.z-dn.net/?f=x%3D-2)
Explanation:
The two equations are
and ![y=-\frac{1}{2} x+2](https://tex.z-dn.net/?f=y%3D-%5Cfrac%7B1%7D%7B2%7D%20x%2B2)
Let us determine the value of the x - coordinate using the substitution method.
Let us substitute
in the equation
, we get,
![3x+3(-\frac{1}{2} x+2)=3](https://tex.z-dn.net/?f=3x%2B3%28-%5Cfrac%7B1%7D%7B2%7D%20x%2B2%29%3D3)
Multiplying the term 3 within the bracket, we get,
![3x-\frac{3}{2} x+6=3](https://tex.z-dn.net/?f=3x-%5Cfrac%7B3%7D%7B2%7D%20x%2B6%3D3)
Subtracting both sides of the equation by 6, we get,
![3x-\frac{3}{2} x=-3](https://tex.z-dn.net/?f=3x-%5Cfrac%7B3%7D%7B2%7D%20x%3D-3)
Taking LCM on the LHS of the equation, we get,
![\frac{6x-3x}{2} =-3](https://tex.z-dn.net/?f=%5Cfrac%7B6x-3x%7D%7B2%7D%20%3D-3)
Subtracting the numerator, we have,
![\frac{3x}{2}=-3](https://tex.z-dn.net/?f=%5Cfrac%7B3x%7D%7B2%7D%3D-3)
Multiplying both sides of the equation by 2, we have,
![3x=-6](https://tex.z-dn.net/?f=3x%3D-6)
Dividing both sides of the equation by 3, we get,
![x=-2](https://tex.z-dn.net/?f=x%3D-2)
Thus, the x - coordinate of the solution is ![x=-2](https://tex.z-dn.net/?f=x%3D-2)