# How do you solve the linear equation y= -2/3x and 2x+3y=5 using the substitution method and are they dependent, independent, or inconsistent?

Feb 10, 2018

1) plug in -2/3x for y in the second equation
2) they are inconsistent

#### Explanation:

To use substitution, solve for a variable in one equation and use it to find the other variable. Since y is already solved for in the first equation, plug -2/3x in as y in the second equation.

$2 x + 3 \left(- \frac{2}{3} x\right) = 5$ $\rightarrow$ distribute
$2 x - 2 x = 5$ $\rightarrow$ simplify
$0 = 5$ $\rightarrow$ inconsistent

When a system is inconsistent, it means that the lines never intersect. When you arrive at a false statement, it means that the lines never intersect; therefore they are inconsistent.

Here's a graph if you need to see it:
Graph