How do you solve the following system?: #5x + 2y =1 , -8x+3y=12#

1 Answer
Jun 23, 2017

Answer:

#(-21/31, 68/31)#

Explanation:

#5x+2y=1#
#-8x+3y=12#

The best way to solve this system of equations is by using the elimination method. Basically, we need to eliminate a variable by adding the two equations together.

However, to completely cancel out a variable, such as #x#, they need to have the same coefficient but different signs (positive and negative).

#8(5x+2y)=(1)8#
#5(-8x+3y)=(12)5#

#40x+16y=8#
#-40x+15y=60#

By multiplying the equations, we can now safely eliminate #x# from the system by adding the two equations together.

#31y=68#

#y=68/31#

Now, you have to plug #y# back into one of the equations to get #x#.

#5x+2(68/31)=1#

#5x+136/31=1#

#5x=1-136/31#

#5x=-105/31#

#x=-105/31 * 1/5#

#x=-21/31#

Here's your answer:

#(-21/31, 68/31)#