How do you solve the following system: #x + 4y = -2 , 5x - 7y = 12 #?

1 Answer
Dec 9, 2015

Answer:

The solution for the system of equations is

#color(blue)(x=-142/27, y=22/27#

Explanation:

#x+4y=-2#, multiplying the equation by #5#
#color(blue)(5x)+20y=-10#....equation #(1)#

#color(blue)(5x) -7y=12#.............equation #(2)#

Solving by elimination :

Subtracting equation #2# from #1#

#cancelcolor(blue)(5x)+20y=-10#

#cancelcolor(blue)(-5x) +7y=-12#

#27y=-22#

#color(blue)(y=22/27#

Finding #x# by substituting #y# in equation #1#:
#x+4y=-2#

#x=-2-4y#

#x=-2-4 * (22/27)#

#x=-2-(88/27)#

#x=-54/27-(88/27)#

#color(blue)(x=-142/27#