How do you solve the system of equations by graphing and then classify the system as consistent or inconsistent #x+2y=6# and #x+2y=-2#?

Answer 1

It is inconsistent.

We can immediately see that we are dealing with two parallel lines. If you write them in the form:

#y=mx+c#

where #m=#slope and #c=# y-intercept, you get:

#y_1=-1/2x+3#

and

#y_2=-1/2x-1#

so that both lines have the same slope #m=-1/2# (same inclination), different y-intercept and will never meet each other!

Graphically:

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Answer 2

To solve the system of equations by graphing, plot the lines corresponding to each equation on the same coordinate plane. Then, determine the point of intersection, if it exists.

For the equations (x + 2y = 6) and (x + 2y = -2):

  • The first equation can be rearranged as (y = \frac{6 - x}{2}), and the second equation can be rearranged as (y = \frac{-2 - x}{2}).

Plotting the lines, you will notice that they are parallel, since they have the same slope ((-\frac{1}{2})) but different y-intercepts. Therefore, there is no point of intersection, indicating that the system is inconsistent.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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