How do solve the following linear system?: # 7x+2y=2 , 8x+2y=3 #?

2 Answers
May 24, 2018

Answer:

The solution is #{(y=-5/2),(x=1):}#

Explanation:

Solve the equations as follows

#{(7x+2y=2),(8x+2y=3):}#

#(2)-(1)#, #=>#, #{(7x+2y=2),(x=1):}#

#<=>#, #{(y=(2-7x)/2),(x=1):}#

#<=>#, #{(y=(2-7)/2),(x=1):}#

#<=>#, #{(y=-5/2),(x=1):}#

May 24, 2018

Answer:

See explanation.

Explanation:

The original system is:

#{(7x+2y=2),(8x+2y=3):}#

We can easily notice that #y# has the same coefficient in both equations, so if we multiply any of the equations by #-1# the coefficients will be opposite numbers. I multiplied the first equation and got:

#{(-7x-2y=-2),(8x+2y=3):}#

Now if we add both sides of the equations we get an equation with one variable only (#x#):

#x=1#

Now we have to substitute the calculated value of #x# to calculate #y#:

#8+2y=3#

#2y=-5#

# y=-2.5#

The solution of the system is:

#{(x=1),(y=-2.5):}#