SOLUTION: Use linear combinations to solve the system of linear equations. 3b+2c=46 5c+b=11

Question 176235: Use linear combinations to solve the system of linear equations.
3b+2c=46
5c+b=11
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Start with the second equation.

Rearrange the terms.

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.

Simplify.

Divide both sides by to isolate .

Reduce.

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

Now go back to the first equation.

Plug in .

Multiply.

Add to both sides.

Combine like terms on the right side.

Divide both sides by to isolate .

Reduce.

So our answer is and .

This means that the system is consistent and independent.

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