Solve the system of equations by graphing. Be sure to identify any solution

Question

y = 2x + 1
Y = -4x + 7

Answer 1

To solve by graphing:

 

   the first line (0,1) , (1,3) , (2,5), (3, 6),   two up, and one to the left

 

   the second line (0,7), (1,3) (2,-1), (3,-5),  four down and one to the left

 

Notice that (1,3) appears on both lines.

That is where they intersect.

 

Now we do it algebraically:

 

 

2x + 1 = -4x + 7

 

Moving everything to left side, changing the signs

 

2x + 1 + 4x - 7 = 0

 

6x - 6 = 0

 

6x = 6

 

x = 1

 

Plugging in X=1 into the equations:

 

 2*x + 1 = 2*1 + 1 = 2 + 1 = 3

-4*x + 7 = -4 * 1 + 7 = -4 + 7 = 3

 

 

So the lines intersect at (x=1, y = 3)