How do you solve the system #x+y=6# and #x-y=2# by graphing?

1 Answer
Tony B
Jun 24, 2016

The common point ( point of intersection) is: #(x,y)->(4,2)#

Explanation:

Simultaneous equations are such that (normally) they plot a range of value that are different to each other. That is, until they cross . At that instant the both have the same values for #x" and "y#. They must have to be able to 'occupy' the same point. For some equation types it can be more than one point and for others, no point at all.

#color(blue)("To determine value of "x)#

Write as:

#x+y=6#
#ul(x-y=2)" "larr" add to and up with only 1 unknown"#
#2x+0=8#

Divide both sides by 2

Thus #x=4#
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

#color(blue)("To determine value of "y)#

Substitute #x=4# into #x+y=6" "#giving:

#color(brown)(x+y=6) " "color(blue)(->" "4+y=6)#

Subtract 4 from both sides

#color(brown)(4color(blue)(-4)+y=6color(blue)(-4))#

#0+y=2#

#y=2#
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Tony B

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