How do solve the following linear system?: #-2x + 1 = 2y, 7x - 4y - 13 = 0 #?

1 Answer
Oct 8, 2017

Answer:

Answer: #(15/11,-19/22)#

Explanation:

Solve by substitution: #-2x+1=2y#, #7x-4y-13=0#

First, we can solve for #y# in the first equation* by dividing both sides by #2#:
#-2x+1=2y#

#y=(-2x+1)/2#

We can now substitute this #y# term into the second equation and solve for #x#:
#7x-4y-13=0#

#7x-4((-2x+1)/2)=13#

Notice that we can cancel a #2# from the numerator and denominator:
#7x-2(-2x+1)=13#

#7x+4x-2=13#

Combining #x#-terms and moving all constants to one side, we find the value of #x#:
#11x=15#

#x=15/11#

To solve for #y#, we plug in the #x# value we just found into the first equation which we solved for #y# and solve for the #y# value which corresponds with #x=15/11#:
#y=(-2x+1)/2#

#=(-2(15/11)+1)/2#

#=((-30)/11+1)/2#

#=((-30+11)/11)/2#

#=-19/22#

Therefore, the solution to the linear system of equations is #(15/11,-19/22)#

*This was chosen because we can see that if we solve for #y# in the first equation and plug into the second equation, the #1/2# resulting from dividing the first equation by #2# would cancel out with the #4# in the second equation when we substitute in (since #2# is a factor of #4#). Solving for any other variable and substituting into the other equation would result in some unwanted fraction which would thus complicate the problem a bit more than necessary.