How do you solve the system #-2x+15y=-24, 2x+9y=24#?

1 Answer
Nov 30, 2016

Answer:

#x = 12# and #y = 0#

Explanation:

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

#-2x + 15y - 15y = -24 - 15y#

#-2x = -24 - 15y#

#(-2x)/-2 = (-24 - 15y)/-2#

#x = 12 +15/2y#

Step 2) Substitute #12 + 15/2y# for #x# in the second equation and solve for #y#:

2(12 + 15/2y) + 9y = 24#

24 + 15y + 9y = 24#

#24 + 24y = 24#

#24 - 24 + 24y = 24 - 24#

#24y = 0#

#(24y)/24 = 0/24$

#y = 0#

Step 3) Substitute #0# for #y# in the solution to the equation in Step 1) and calculate #x#:

#x = 12 + (15/2 * 0)#

#x = 12 + 0#

#x = 12#