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

Algebra ->  Equations -> 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       Log On


   

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) About Me  (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:


system%282x%2B3y=2%2C7x-y=3%29


3%287x-y%29=3%283%29 Multiply the both sides of the second equation by 3.


21x-3y=9 Distribute and multiply.


So we have the new system of equations:
system%282x%2B3y=2%2C21x-3y=9%29


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


%282x%2B3y%29%2B%2821x-3y%29=%282%29%2B%289%29


%282x%2B21x%29%2B%283y-3y%29=2%2B9 Group like terms.


23x%2B0y=11 Combine like terms. Notice how the y terms cancel out.


23x=11 Simplify.


x=%2811%29%2F%2823%29 Divide both sides by 23 to isolate x.


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


2x%2B3y=2 Now go back to the first equation.


2%2811%2F23%29%2B3y=2 Plug in x=11%2F23.


22%2F23%2B3y=2 Multiply.


22%2B69y=46 Multiply EVERY term by the LCD 23 to clear the fraction


69y=46-22 Subtract 22 from both sides.


69y=24 Combine like terms on the right side.


y=%2824%29%2F%2869%29 Divide both sides by 69 to isolate y.


y=8%2F23 Reduce.


So the solutions are x=%2811%29%2F%2823%29 and y=8%2F23