Question

Graph the following system of equations and find the x-coordinate of the solution.

Answer 1

The x - coordinate of the solution is $x=-2$

Explanation:

The two equations are $3 x+3 y=3$ and $y=-\frac{1}{2} x+2$

Let us determine the value of the x - coordinate using the substitution method.

Let us substitute $y=-\frac{1}{2} x+2$ in the equation $3 x+3 y=3$, we get,

$3x+3(-\frac{1}{2} x+2)=3$

Multiplying the term 3 within the bracket, we get,

$3x-\frac{3}{2} x+6=3$

Subtracting both sides of the equation by 6, we get,

$3x-\frac{3}{2} x=-3$

Taking LCM on the LHS of the equation, we get,

$\frac{6x-3x}{2} =-3$

Subtracting the numerator, we have,

$\frac{3x}{2}=-3$

Multiplying both sides of the equation by 2, we have,

$3x=-6$

Dividing both sides of the equation by 3, we get,

$x=-2$

Thus, the x - coordinate of the solution is $x=-2$