Respuesta :
The x - coordinate of the solution is [tex]x=-2[/tex]
Explanation:
The two equations are [tex]$3 x+3 y=3$[/tex] and [tex]y=-\frac{1}{2} x+2[/tex]
Let us determine the value of the x - coordinate using the substitution method.
Let us substitute [tex]y=-\frac{1}{2} x+2[/tex] in the equation [tex]$3 x+3 y=3$[/tex], we get,
[tex]3x+3(-\frac{1}{2} x+2)=3[/tex]
Multiplying the term 3 within the bracket, we get,
[tex]3x-\frac{3}{2} x+6=3[/tex]
Subtracting both sides of the equation by 6, we get,
[tex]3x-\frac{3}{2} x=-3[/tex]
Taking LCM on the LHS of the equation, we get,
[tex]\frac{6x-3x}{2} =-3[/tex]
Subtracting the numerator, we have,
[tex]\frac{3x}{2}=-3[/tex]
Multiplying both sides of the equation by 2, we have,
[tex]3x=-6[/tex]
Dividing both sides of the equation by 3, we get,
[tex]x=-2[/tex]
Thus, the x - coordinate of the solution is [tex]x=-2[/tex]
