How do you solve the following linear system: #y=-x+4, 3x+y=-2#?

1 Answer
Mar 11, 2018

Answer:

#x=-3 and y=7#

Explanation:

This is one of the best forms you can have for a system of equations. Note that they each have a single #y# term...

Graphically it means they each represent a straight line and the solution is the point of intersection of the lines.

Write each equation in slope-intercept form, ie with #y# on one side.

#y = -x+4 " and "y= -3x-2#

Now, as #y = y#, equate the right sides of the equations:

#-x+4 =-3x-2#

#3x-x=-2-4#

#2x = -6#

#x=-3#

Now you can use one equation to find a value for #y# and the
other equation to check.

#y = -(-3)+4" "and" "y =-3(-3)-2#
#y= 3+4color(white)(wwwwwwwwwwww.w)y = 9-2#
#y =7color(white)(wwwwwwwwwwwwwwww)y=7#