How do you solve #4x - y = 6# and #3x + y = 1#?

1 Answer
Feb 11, 2016

Answer:

#x=1,y=-2#

Explanation:

Notice that when the two equations are added to one another, the #y# and #-y# terms will cancel. This is opportune because we will be left with just #x# terms.

Add the two equations:

#{:(color(white)("(")4x,-y,=6," "),("("3x,+y,=1")",+),(color(white)("(")color(blue)(7x),cancel(+0y),color(blue)(=7)," "):}#

The resulting equation #7x=7# can be divided by #7# on both sides:

#(7x)/7=7/7" "" "=>" "" "color(red)(x=1#

This can be substituted into either equation to solve for #y#. I'll choose the second equation.

#3color(red)x+y=1" "" "=>" "" "3color(red)((1))+y=1#

Solve the resulting equation:

#3+y=1#

#color(green)(y=-2#