# 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#?

##### 1 Answer

Jan 8, 2018

#### Answer:

#(3,0)#

#### Explanation:

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)#

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