Determine if the solution set for the system of equations shown is the empty set, contains one point or is infinite.
2x - y = 7
2y = 4x - 14

Question

Determine if the solution set for the system of equations shown is the empty set, contains one point or is infinite.
2x - y = 7
2y = 4x - 14

directrix · Answer

2x - y = 7
 2y = 4x - 14

Line up like variables.

anonymous · Answer

Would it be 1 solution?

directrix · Answer

2x   - y = 7
-4x +2y = -14
--------------

directrix · Answer

@kbriones0 

Multiply the top equation by 2

2x - y = 7  --> by  2 is what?

anonymous · Answer

14?

directrix · Answer

No.

2x - y = 7 --> by 2 --->  4x -2y = -14

Add that to the second equation

anonymous · Answer

ok im with you

directrix · Answer

4x -2y = 14
-4x +2y = -14
-------------      Add those two equations. What do you get.

directrix · Answer

>Would it be 1 solution?   NO

directrix · Answer

Look at the attached chart after you add the two equations.

anonymous · Answer

8x-4y-14=0?

directrix · Answer

No. 0 + 0 = 0

4x -2y = 14 is the same line as -4x +2y = -14.

If you multiply -4x +2y = -14 by -1, you will get the first equation.

So, there is only one line here.

Or, you can  say that they coincide in every point.

directrix · Answer

Your equations intersect in every point. Look on the attached chart and read how many solutions there are. That is the answer to this question.

anonymous · Answer

Oh okay. Thank you so much

directrix · Answer

You are welcome.