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

Question

Eli Assouline · Accepted Answer

#(1.5, 0)#

Thus, you can first configure your linear system as follows:

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

Proceed with this as it will simplify the next few steps more visually.

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#

Simplified, you ought to receive the following:

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

Subsequently, combine the equations in a vertical manner, ensuring that the addition is limited to the respective 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#

Next, make it simpler:

#2x = 3#

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

#x = 3/2 = 1.5#

Lastly, you enter them into a coordinate point designating the intersection of the two equations:

#(1.5, 0)#

Avery Alexander · Answer

undefined To solve the linear system:
2x - 4y = 3
2x - 5y = 3

Subtract the second equation from the first equation:
2x - 4y - (2x - 5y) = 3 - 3
Simplify:
2x - 4y - 2x + 5y = 0
Combine like terms:
-4y + 5y = y
y = 0

Substitute y = 0 into either equation to solve for x:
2x - 5(0) = 3
2x = 3
x = 3/2

So, the solution to the linear system is:
x = 3/2
y = 0