How do you solve the system of equations: 4x+3y=7 and -2x+y=9?

1 Answer
Aug 8, 2015

Answer:

The solution for the system of equations is:
#color(blue)(x=-2, y=5#

Explanation:

#color(blue)(4x)+3y=7 #............equation #(1)#

#-2x+y=9#, multiplying this equation by #2#
#color(blue)(-4x)+2y=18#......equation #(2)#

Now, we can solve the system of equations through elimination.
Adding the two equations eliminates #color(blue)(4x#

#cancelcolor(blue)(4x)+3y=7 #
#cancelcolor(blue)(-4x)+2y=18#

#5y=25#

#color(blue)(y=5#

Now, we find #x# by substituting the value of #y# in equation #1#:

#4x+3y=7 #

#4x=7-3y #

#x=(7-3y)/4#

#x=((7-3*5))/4#

#x=((7-15))/4#

#x=-8/4#

#color(blue)(x=-2#