How do you solve the system of equations #2x + 5y = - 17# and #3x + 8y = - 29#?

Question

754 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-11-23T15:05:12

#y = -7# and #x = 9#

Step 1) Solve the second equation for #x#:

#3x + 8y - 8y = -29 - 8y#

#3x = -29 - 8y#

#(3x)/3 = (-29 - 8y)/3#

#x = -29/3 - (8y)/3#

Step 2) Substitute #-29/3 - (8y)/3# for #x# in the first equation and solve for #y#:

#2(-29/3 - (8y)/3) + 5y = -17#

#(-58)/3 - (16y)/3 + 5y = -17#

#(-58)/3 - (16y)/3 + (15y)/3 = -17#

#(-58)/3 - (1y)/3 = -17#

#3*((-58)/3 - (1y)/3) = -17 * 3#

#-58 - y = -51#

#-58 - y + y + 51 = -51 + y + 51#

#-7 = y# or #y = -7#

Step 3) Substitute #-7# for #y# in the solution for the second equation:

#x = -29/3 - (8 * -7)/3#

#x = -29/3 - (-56)/3#

#x = -29/3 + 56/3#

#x = 27/3#

#x = 9#