How do you solve the system of equations by graphing and then classify the system as consistent or inconsistent #5x - y = -9# and #y + 2x = 2#?

1 Answer

Answer:

#x=-1#
#y=4#

Explanation:

Determine the intercepts then connect the points to draw the lines.
For #5x-y=-9#
When #x=0#, #y=9#
#(0, 9)# is point on the line #5x-y=-9#

When #y=0#, #x=-9/5#
#(-9/5, 0)# is a point on the line #5x-y=-9#

Draw the line passing thru #(0, 9)# and #(-9/5, 0)#

~~~~~~~~~~~~~~~~~~~~~~~~~~~
For #2x+y=2#
When #x=0#, #y=2#
#(0, 2)# is point on the line #2x+y=2#

When #y=0#, #x=1#
#(1, 0)# is a point on the line #2x+y=2#

Draw the line passing thru #(0, 2)# and #(1, 0)#

~~~~~~~~~~~~~~~~~~~~~~~~~~~
The two lines intersect at #(-1, 4)#

The system is consistent.

Kindly see the graphs
Desmos.com

God bless....I hope the explanation is useful.