How do you solve the system of equations by graphing and then classify the system as consistent or inconsistent #2x+y=0# and #5x-y=7#?

1 Answer

Answer:

graph{(2x+y)(5x-y-7)=0 [-10, 10, -5, 5]}
#color(red)(x=1# #&# #color(magenta)(y=-2#

Explanation:

#5x-y=7#
#y=5x-7#

Given that, #2x+y=0#

Replacing, #y=5x-7# in #2x+y=0#

#2x+(5x-7)=0#

#7x-7=0#

#7x=7#

#color(red)(x=1#

Replacing #x=1#, in #y=5x-7#

#y=5xx1-7#

#color(magenta)(y=-2#

The values are consistent.

Alternatively ,
Consider #y=5x-7# and plot the points on the graph that satisfy the equation, such as #(0,-7), (2,3)#etc
and for #2x+y=0#, you could plot #(0,0), (2,-2)# etc

You would get two lines in the graph. Mark the point of intersection and that's the solution for the equations.
Here, the lines meet at (1,-2). Therefore the solution is, #x=1, y=-2# (which matches the answer above:) )

P.S. to get the points to plot on the graph for both the equations, replace #x# as any value and then get the corresponding value of #y# from the equality.

~Hope this helps!