Answer
True for all values of $x$ and $y$.
Work Step by Step
equation 1 $$4y = 2x + 6$$ equation 2 $$x - 2y = -3$$
Using equation 2, add $2y$ to both sides:
$$x - 2y = -3$$ $$x - 2y +2y= -3+2y$$ $$x = -3+2y$$
We will refer to $x = -3+2y$ as equation $2'$.
Substitute equation 2' to equation 1:
$$4y = 2x + 6$$ $$4y = 2(-3+2y) + 6$$ $$4y = -6+4y + 6$$ $$4y = 4y$$
Since the equation is true, then the equation is true for all values of $y$.
Now, let's solve for $x$.
Using equation 2, subtract $x$ from both sides:
$$x - 2y = -3$$ $$x -x- 2y = -3-x$$ $$- 2y = -3-x$$ Divide both sides by $-2$.
$$\frac{-2y}{-2} = \frac{-3-x}{-2}$$ $$y=\frac{-3-x}{-2}$$ $$y=\frac{3+x}{2}$$
Substitute this to equation 1:
$$4y = 2x + 6$$ $$4(\frac{3+x}{2}) = 2x + 6$$ $$2(3+x)= 2x + 6$$ $$6+2x= 2x + 6$$
Hence, the equation is also true for all values of $x$.