How do you solve the system of equations by graphing and then classify the system as consistent or inconsistent #3x-y=9# and #2x+y=6#?

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Answer 1 · 2018-01-08T09:55:58

#(3,0)#

Given -

#3x-y=9# -------------(1)
#2x+y=6# -------------(2)

If the slopes are different, both are consistent, else inconsistent.

When the equations are in the form

#ax+by =c#
The formula for slope is #m=- a/b#
Slope of the first line #m_1=- 3/(-1)=3#
Slope of the second line #m_2=- 2/1=2#

The slopes are different. They are consistent.

We have to find the intercepts for the two lines to graph them

y-intercept of the 1st line

#3(0)-y=9#
#y=-9#
#(0, -9)#

x-intercept of the 1st line

#3x-(0)=9#
#x=9/3=3#
#(3,0)#

y-intercept of the 2nd line

#2(0)+y=6#
#y=6#
#(0,6)#

x-intercept of the 2nd line

#2x+0=6#
#x=6/2=3#
#(3, 0)#

[#(3, 0)# is a common point for both the lines. Hence it is the solution]

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