How do you solve the system #y = 3x - 4# and #2x - y = 1# by graphing?

1 Answer
Andy Y.
Mar 15, 2016

Solution: #x=3# and #y=5#

Explanation:

Step one. Solve both equations for #y#. The first equation you provided is already equal to #y#, so just copy it.

Then solve the second equation for #y#:

#2x-y=1#
#color(white)(..)+ycolor(white)(.)+y# #color(white)(..x)#add y to both sides
#2x=1+y#
#-1color(white)(.)-1# #color(white)(xxxx;)#subtract 1 from both sides
#2x-1=y#

Now, either plotting points or plugging into your graphing utility, you can first graph the first equation:

# graph{3x-4 [-1, 3, -6, 10]} #

Then, on the same graph paper, either plot points or plugging into your graphing utility, you draw the second graph on top of this one.

# graph{(y-2x+1)(y-3x+4)=0 [-0.4,4.5,-2,8]} #

Observing closely where they cross, gives the solution

#x=3# and #y=5#.

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