How do you solve the system of equations by graphing and then classify the system as consistent or inconsistent y=-x-1 and y=2x+14?

Dec 5, 2017

Explanation:

We are given systems of two linear equations in two variables:

$y = - x - 1 \mathmr{and}$

$y = 2 x + 14$

These can be visually represented by simultaneously graphing both the equations.

The system can be Consistent or Inconsistent and the equations in the system can either be Dependent or Independent.

A system which has No Solutions are said to be Inconsistent.

A system with one or more solutions are called Consistent, having either one solution or an infinite number of solutions.

We are given systems of two linear equations in two variables:

$y = - x - 1 \mathmr{and}$ $. . \textcolor{red}{E q n .1}$

$y = 2 x + 14$ $. . \textcolor{red}{E q n .2}$

If you refer to the graph available with this solution, you can observe two distinct intersecting straight lines: one $\textcolor{b l u e}{B l u e}$ Line and one $\textcolor{red}{R e d}$ Line.

We get a pair of $\left(x , y\right)$ which is the single unique solution for the system of equations.

As you can observe, the intersection point has coordinates $\left(- 5 , 4\right)$

Our system of equations is therefore a Consistent System of Independent Equations.

The solution set has single ordered pair $\left(- 5 , 4\right)$

Our equations are in the Slope-Intercept Form:

Slope-Intercept Form is written as $y = m x + b$

$m$ is the Slope and $b$ is the y_intercept

We note that the Slope is different for each equation.

The system has one unique solution and therefore is a consistent system.

The equations are also Independent, as each equation is describing a different straight line.

I hope this helps.