How do solve the following linear system?: # 2x - 4y =3, 2x - 5y=3 #?

So first you can set up your linear system to the following:

#{(2x - 4y = 3), (2x - 5y = 3) :}#

Do this because it is visually easier to simplify the next couple steps.

For the simplification part, I will be using the elimination method on the #x# variables so that we can obtain a #y# variable answer.

Multiply the top equation in the linear system by #-1#

#-1(2x - 4y = 3)#
#2x - 5y = 3#

You should get the following when simplified:

#{(-2x + 4y = -3), (2x - 5y = 3) :}#

Next, add the equations together going vertically making sure to add only to the corresponding term.

The #x# values and the numerical values should be equal to #0# when this is done correctly and you should be left with the following:

#-y = 0#

Then simplify by dividing the #-1# coefficient from #y#:

#y = 0#

Then you plug the #y# value back into one of the original equations:

#2x - 4(0) = 3#

Then simplify:

#2x = 3#

Divide the #2# coefficient from the #x# and you should be just left with

#x = 3/2 = 1.5#

Finally, you plug them into a coordinate point that indicates when the two equations intersect:

#(1.5, 0)#