# How do you solve the system of equations by graphing and then classify the system as consistent or inconsistent x+2y=4 and 2x+4y=8?

Jun 24, 2018

dependent consistent equations and there are infinite no. of solutions for "x" and "y" in this system of equations

#### Explanation:

We have
(a):=$x + 2 \cdot y = 4$ and (b):=$2 \cdot x + 4 \cdot y = 8$
dividing (b) both sides by two we get
(b)=$x + 2 \cdot y = 4$
we see that both the equations are same
then there are infinite no. of solution for "x" and "y"

Again,
now taking the ratios of the coefficients of ${x}^{2}$ and x and the constant terms one by one we get

$\frac{1}{2}$(coefficients of ${x}^{2}$
$\frac{2}{4} \implies \frac{1}{2}$(coefficients of x)
$\frac{4}{8} \implies \frac{1}{2}$(constant terms)
we see that the all the three ratio is same hence the equations will have infinite no. of common solution or we can say that both are coinciding with each other
Such type of equations is known as dependent consistent equations

Now, if first two ratio matches but the third is different then the lines are parallel with no common solution.They are known as inconsistent equations

And if none of the ratio is matching then they are intersecting lines and they will have a unique solution.They are known as independent consistent equations