How do you solve the system by graphing #2x + 4y =2# and #x + 2y = 1#?

1 Answer
Jan 29, 2018

Answer:

See below...

Explanation:

To solve this we must graph each of the lines:

First line: #2x+4y=2 #

Rearange:

#4y = 2 - 2x#

#=> y = 1/2 - 1/2x #

Now we need to plot two or three points that lie on the line:

We need to find #y# at some #x# values:

At #x = 1# , #y = 1/2 - (1/2*1)= 1/2 - 1/2 = 0 #

At #x = -1 # , # y = 1/2 - (1/2*-1) = 1/2 +1/2 = 1#

Hence these are two points that lie on the line:

#color(blue)( (1,0) # and #color(red)( (-1,1) #

enter image source here

Hence connecting them up to give a line:

enter image source here

Now we can do this whole procces for the second line, graphing them on the same graph we see:

enter image source here

#color(red)( underline( "They are the same line! " ) ) #

When we deal with these roblems, the solution is where the lines intersect, where they meet

They meet at all points, as they are the same:

#color(red)("The solutions to this system is all the points that lie on"#
#color(red)(-> 2x+4y=2#