How do you solve #x + y = 10 # and #x - y = 8#?

Question

10463 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2015-08-06T09:36:01

#{(x = 9), (y=1) :}#

The easiest way in which you can solve this system of equations is to add the two equations to get the value of #x#.

More specifically, you add the left side of the equations and the right side of the equations separately.

#{(x+y = 10), (x-y = 8) :}#

#x + color(red)cancelcolor(black)(y) + x - color(red)cancelcolor(black)(y) = 10 + 8#

#2x = 18 implies x= 18/2 = color(green)(9)#

Now use the value of #x# in one of the two equations to get the value of #y#

#9 + y = 10 implies y = 10 - 9 = color(green)(1)#