How do solve the following linear system?: # -2x+3y=-1 , -x-7y=14 #?

1 Answer
Aug 29, 2016

Answer:

First, solve equation #2 for x.

Explanation:

This gives you #x = - 7y - 14# .

Now substitute this value of x into the 1st equation, like this:

#-2(-7y-14)+3y=-1#

Multiply the negative 2 into the parentheses:

#14y+28+3y=-1#

Combine like terms:

#17y+28=-1#

Move the 28 to the other side of the equation:

#17y=-29#

Divide both sides by 17 to isolate the y-term:

#17y/17=-29/17#

which gives you:

#y=-29/17#.

Since 17 and 29 are both prime numbers, the answer cannot be reduced.

Now you have the value of y. Plug that into the either eqn:

#-2x +3(-29/17)=-1#

and solve for x.

#-2x-87/17=-1#
#-2x=-1+87/17=70/17#

Divide both sides by negative 2:
#x=(70/17)/-2=70/17*(-1/2)=-70/34#

Reduce:
#x=-35/17#

Now plug #x=-35/17# and #y=-29/17# into either eqn to check the answers:

Does #-2(-35/17)+3(-29/17)=-1# ?
#70/17-87/17=-1# ?
#-17/17=-1#

The fractions look odd, but it checks out.