# How do you solve 3x - y = 3, 2x + y = 2 by graphing and classify the system?

Aug 27, 2017

See a solution process below:

#### Explanation:

For each equation we need to solve for two points which solve the equation and plot these points and then draw a line through the points:

Equation 1:

First Point:
For $x = 0$

$\left(3 \cdot 0\right) - y = 3$
$0 - y = 3$
$- y = 3$
$\textcolor{red}{- 1} \cdot - y = \textcolor{red}{- 1} \cdot 3$
$y = - 3$ or $\left(0 , - 3\right)$

Second Point:
For $y = 0$

$3 x - 0 = 3$
$3 x = 3$
$\frac{3 x}{\textcolor{red}{3}} = \frac{3}{\textcolor{red}{3}}$
$x = 1$ or $\left(1 , 0\right)$

graph{(3x-y-3)(x^2+(y+3)^2-0.075)((x-1)^2+y^2-0.075)=0 [-20, 20, -10, 10]}

Equation 2:

First Point:
For $x = 0$

$\left(2 \cdot 0\right) + y = 2$
$0 + y = 2$
$y = 2$ or $\left(0 , 2\right)$

Second Point:
For $y = 0$

$2 x + 0 = 2$
$2 x = 2$
$\frac{2 x}{\textcolor{red}{2}} = \frac{2}{\textcolor{red}{2}}$
$x = 1$ or $\left(1 , 0\right)$

graph{(2x+y-2)(3x-y-3)(x^2+(y-2)^2-0.075)((x-1)^2+y^2-0.075)=0 [-20, 20, -10, 10]}

We can see the points cross at $\left(1 , 0\right)$

graph{(2x+y-2)(3x-y-3)((x-1)^2+y^2-0.05)=0 [-10, 10, -5, 5]}

A system of two linear equations can have one solution, an infinite number of solutions, or no solution. Systems of equations can be classified by the number of solutions. If a system has at least one solution, it is said to be consistent . If a consistent system has exactly one solution, it is independent.

This system is an independent consistent system.