SOLUTION: Solve the system of equations by the method of your choice. Are the equations independent, dependent, or inconsistent? x + y=4 and x-y=5? Thank you Shelley

Question 330295: Solve the system of equations by the method of your choice. Are the equations independent, dependent, or inconsistent?
x + y=4 and x-y=5?
Thank you
Shelley
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!

Start with the given system of equations:

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.

Simplify.

Divide both sides by to isolate .

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

Now go back to the first equation.

Plug in .

Multiply both sides by the LCD to clear any fractions.

Distribute and multiply.

Subtract from both sides.

Combine like terms on the right side.

Divide both sides by to isolate .

So the solutions are and .

Which form the ordered pair

.

This means that the system is consistent and independent.

RELATED QUESTIONS
Solve the system of equations by the method of your choice: 6x + 3y = 9 and y = � 2x... (answered by solver91311,mananth)

Please solve the system of equations by the method of your choice: 2x-4y=6 and 4x+y=21 (answered by stanbon)

Please solve the system of equations by the method of your choice: 6x+3y=9 and y=-2x+2 (answered by Fombitz)

Solve the system of linear equations by the substitution method. Then, state whether the (answered by nabla)

Solve the system of equations by graphing. Then classify the system as consistent or... (answered by jim_thompson5910)

Solve each system by the substitution method. Determine whether the equations are... (answered by sofiyacherni)

Solve each system by substitution. Determine whether the equations are independent,... (answered by Mathtut)

Solve each system by substitution. Determine whether the equations are independent,... (answered by Fombitz)