How do you solve the system #x + y - 6 = 0# and #x - y = 0# by graphing?

1 Answer
Alan P.
Jan 14, 2016

Draw the lines for the linear equations given and note the point at which the two line insect (in this case at #(x,y) = (3,3)# ).

Explanation:

The easiest points to use for graphing purposes are often the intercepts.

For #color(blue)(x+y-6=0)#
the intercepts are at #(color(blue)(0,6) )# and #(color(blue)(6,0))#

For #color(red)(x-y=0)#
the x and y-intercepts are the same point: #(color(red)(0,0))#
so it will be necessary to pick one more point;
since we already have a #6# lets pick #x=6# which given the equation implies #y=6# and we have a second point #(color(red)(6,6))#

Drawing a line connecting
#color(white)("XXX")(color(blue)(0,6))# and #(color(blue)(6,0))#
and another connecting
#color(white)("XXX")(color(red)(0,0)# and #(color(red)(6,6))#
gives us a point of intersection at #(color(green)(3,3))#
enter image source here

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