Question

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`?

Answer 1

Please read the explanation and refer to the graph.

Explanation:

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

`y = -x-1 and`

`y = 2x+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 and` `..color(red)(Eqn.1)`

`y = 2x+14` `..color(red)(Eqn.2)`

If you refer to the graph available with this solution, you can observe two distinct intersecting straight lines: one `color(blue)(Blue)` Line and one `color(red)(Red)` Line.

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

As you can observe, the intersection point has coordinates `(-5, 4)`

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

The solution set has single ordered pair `(-5,4)`

Our equations are in the Slope-Intercept Form:

Slope-Intercept Form is written as `y= mx+ 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.