Is the ordered pair (2,2) a solution to the system 2x - y = 2 and x + 3y =8?

1 Answer
May 10, 2016

Answer:

Yes; #(x,y)=(2,2)# is a solution to
#color(white)("XXX")2x-y=2# and
#color(white)("XXX")x+3y=8#

Explanation:

Substituting #(color(red)(2),color(blue)(2))# for #(color(red)(x),color(blue)(y))#

  1. in the expression #2color(red)(x)-color(blue)(y)#
    gives #(2xxcolor(red)(2))+color(blue)(2) = 2#
    So #(color(red)(2),color(blue)(2))# is a solution for #2color(red)(x)-color(blue)(y)=2#
  2. in the expression #color(red)(x)+3color(blue)(x)#
    gives #color(red)(2)+(3xxcolor(blue)(2))=8#
    So #(color(red)(2),color(blue)(2))# is a solution for #color(red)(x)+3color(blue)(y)=8#

Since #(color(red)(2),color(blue)(2))# is a solution for both equations,
it is a solution for the system of equations (since the system is comprised of only those two equations).