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

1 Answer
May 6, 2018

Answer:

#x=1 and y=2#

Explanation:

#color(white)(xxxxx)-6x+6y =6" "....A#
#color(white)(xxxxxxxx)color(blue)(x)+2y=5" "....B#
#Adiv 6 rarr color(blue)(-x)+y =1" "....C#

we now have a perfect scenario where #color(blue)(x) and color(blue)(-x)# are additive inverses. Their sum is #0#
Add the equations #A and C# together.

#A+C rarr color(white)(xxxx)3y=6#
#color(white)(xxxxxxxxxxxx)y=2#

Substitute into #B:" "x+2(2)=5#
#color(white)(xxxxxxxxxxxxxxxxxx)x=1#

Check in #C#

# (-1)+(2) =1" "....C#