How do you solve the system of equations by graphing and then classify the system as consistent or inconsistent #2x - 3y = 14# and #2x + y = -10#?

1 Answer
Aug 21, 2017

Answer:

See a solution process below:

Explanation:

To graph the lines first find two points on the line. Then plot the points. Then draw a line through the points:

Equation 1:

For #x = 1#

#(2 * 1) - 3y = 14#

#2 - 3y = 14#

#-3y = 12#

#y = -4# or #(1, -4)#

For #x = 4#

#(2 * 4) - 3y = 14#

#8 - 3y = 14#

#-3y = 6#

#y = -2# or #(1, -2)#

graph{((x-1)^2+(y+4)^2-0.25)((x-4)^2+(y+2)^2-0.25)(2x-3y-14)=0 [-30, 30, -15, 15]}

Equation 2:

For #x = 0#

#(2 * 0) + y = -10#

#0 + y = -10#

#y = -10# or #(0, -10)#

For #x = -5#

#(2 * -5) + y = -10#

#-10 + y = -10#

#y = 0# or #(-5, 0)#

graph{(2x+y+10)(x^2+(y+10)^2-0.25)((x+5)^2+y^2-0.25)(2x-3y-14)=0 [-30, 30, -15, 15]}

We can see the the lines cross at #(-2, -6)# Because there is on solution the system is consistent.

graph{((x+2)^2+(y+6)^2-0.05)(2x+y+10)(2x-3y-14)=0 [-16, 16, -8, 8]}