How do you solve the system of equations by graphing and then classify the system as consistent or inconsistent #y = -3x - 7# and #-8x + 2y = 1#?

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Answer 1 · 2018-07-12T10:34:15

The solution is #(-15/14,-53/14)# or #~~(-1.07,-3.79)#. Since there is one solution, the system is consistent.

Equation 1: y=-3x-7#

Equation 2: -8x+2y=1#

Equation 1 is already solved for #y#. Substitute #-3x-7# for #y# in Equation 2 and solve for #x#.

#-8x+2(-3x-7)=1#

Expand.

#-8x-6x-14=1#

Add #14# to both sides.

#-8x-6x=1 +14#

Simplify.

#-14x=15#

Divide both sides by #-14#.

#x=-15/14# or #~~-1.07#

Substitute #-15/14# for #x# in Equation 1 and solve for #y#.

#y=-3(-15/14)-7#

Expand.

#y=45/14-7#

Multiply #7# by #14/14# to get an equivalent fraction with #14# as the denominator. Since #n/n=1#, the numbers will change, but not the value.

#y=45/14-(7xx14/14)#

Simplilfy.

#y=45/14-98/14#

Simplify.

#y=-53/14# or #~~3.79#

The solution is #(-15/14,-53/14)# or #~~(-1.07,-3.79)#. Since there is one solution, the system is consistent.

graph{(y+3x+7)(-8x+2y-1)=0 [-10, 10, -5, 5]}