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#?

1 Answer
Dec 5, 2017

Answer:

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.

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