SOLUTION: Solve each system using the indicated method. State wheather the system is consistent or inconsistent and dependent or independent. Must use the addition method. A. x+2y=7

Question 164076: Solve each system using the indicated method. State wheather the system is consistent or inconsistent and dependent or independent. Must use the addition method.
A. x+2y=7
x-y=1
B. 3x-5y=5
-x+y=-1
C. 7x-4y=27
5x+6y=6
D. 2x+3y=8
3x+3y=12
If someone can help me solve one of these, then i can build off of it to hopefully complete the other ones. Thanks and please help
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
I'll do the first two to get you started

A)

Start with the given system of equations:

Multiply the both sides of the second equation by -1. Doing so will make the coefficients of the two x terms be equal but opposite.

Distribute and multiply.

So we have the new system of equations:

Now add the equations together. You can do this by simply adding the two left sides and the two right sides separately like this:

Group like terms.

Combine like terms. Notice how the x terms cancel out.

Simplify.

Divide both sides by to isolate .

Reduce.

------------------------------------------------------------------

Now go back to the first equation.

Plug in .

Multiply.

Subtract from both sides.

Combine like terms on the right side.

So our answer is and .

Which form the ordered pair

.

This means that the system is consistent and independent.

Notice when we graph the equations, we see that they intersect at

. So this visually verifies our answer.

Graph of (red) and (green)

B)

Start with the given system of equations:

Multiply the both sides of the second equation by 3.

Distribute and multiply.

So we have the new system of equations:

Now add the equations together. You can do this by simply adding the two left sides and the two right sides separately like this:

Group like terms.

Combine like terms. Notice how the x terms cancel out.

Simplify.

Divide both sides by to isolate .

Reduce.

------------------------------------------------------------------

Now go back to the first equation.

Plug in .

Multiply.

Subtract from both sides.

Combine like terms on the right side.

Divide both sides by to isolate .

Reduce.

So our answer is and .

Which form the ordered pair

.

This means that the system is consistent and independent.

Notice when we graph the equations, we see that they intersect at

. So this visually verifies our answer.

Graph of (red) and (green)

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