How do you solve the following system: #6x+2y=-4, -x+y=5#?

#6*x+2*y=-4#
#-x+y=5#
multiply 2nd by 2, gives.
#-2*x+2*y=10#
subtract from top.
#8*x=-14#
#x= -14/8=-1.75#
#1.75+y=5#
#y=5-1.75=3.25#
check #6*-1.75+2*3.25=-4#

Solve by elimination and substitution

#color(blue)(6x+2y=-4#

#color(blue)(-x+y=5#

Multiply the second equation by #-2#

#rarr-2(-x+y=5)#

#rarr2x-2y=-10#

Now,eliminate #2y# in the first equation by #-2y# in the second equation

Add both the equations

#rarr(6x+2y=-4)+(2x-2y=-10)#

#rarr8x=-14#

#color(green)(rArrx=-14/8=-7/4#

Now,substitute the value of #x# to the second equation

#rarr-(-7/4)+y=5#

#rarr7/4+y=5#

#color(green)(rArry=5-7/4=13/4#