SOLUTION: Solve each system of equations algebraically using the method of substitution or the method of elimination. If the system has no solution, say it is inconsistent. 2. 2 x + 3y

Question 158049This question is from textbook
: Solve each system of equations algebraically using the method of substitution or the method of elimination. If the system has no solution, say it is inconsistent.
2. 2 x + 3y = 2
7x � y = 3
- y = -7x + 3 then substitute 2x + 3 x -(-7x + 3) = 2, 2x + 21x + 6 = 2, 23x + 6 = 2 Am I headed in the right direction? How do I complete? Stuck This question is from textbook

Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
I'm going to use the elimination method

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 y terms cancel out.

Simplify.

Divide both sides by to isolate .

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

Now go back to the first equation.

Plug in .

Multiply.

Multiply EVERY term by the LCD 23 to clear the fraction

Subtract from both sides.

Combine like terms on the right side.

Divide both sides by to isolate .

Reduce.

So the solutions are and
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