How do you solve the following linear system: # –3x + 2y = 12 , 5x + 2y = -4 #?

1 Answer
Mar 31, 2018

Answer:

#x = -2#
#y= 3#

Explanation:

1. The first step is to find similar coefficients between the two equations. Notice that both equations have a #2y# .

#-3x+ 2y =12#
#5x+ 2y =-4#

2. Because the coefficients are equal and not opposite, you have to times one of the equations by -1. For simplicity, lets use #-3x+ 2y =12#.

#-1*(-3x+ 2y =12)#
#5x+ 2y =-4#

#3x- 2y =-12#
#5x+ 2y =-4#

3. Now that the coefficients in front of #y# are opposite, we can add the two equations and the #y# values would cancel out.

#3x- 2y =-12#
#+#
#5x+ 2y =-4#

#8x=-16#

4. Divide both side by #8# to get the value of #x#.

#x=-2#

5. Substitute the value of #x# into one of the equations. For simplicity, lets use #5x+ 2y =-4# .

#5(-2)+ 2y =-4#

6. Simplify

#-10+ 2y =-4#

7. Add 10 to both sides so that #2y# is alone.

#2y=6#

8. Divide both side by #2# to get the value of #y#.

#y=3#

You now have found both the value of #x# and the value of #y#.

#x = -2#
#y= 3#