How do you solve the system of equations #2x+2y=410# and #15x+30y=2265#?

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Answer 1 · 2016-12-04T21:08:08

#x = 259# and #y = -54#

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

(2x + 2y)/2 = 410/2#

#x + y = 205#

#x + y - y = 205 - y#

#x = 205 - y#

Step 2) Substitute #25 - y# for #x# in the second equation and solve for #y#:

#15(205 - y) + 30y = 2265#

#3075 - 15y + 30y = 2265#

#3075 + 15y = 2265#

#3075 - 3075 + 15y = 2265- 3075#

#15y = -810#

#(15y)/15 = -810/15#

#y = -54#

Step 3) Substitute #-54# for #y# in the solution to the first equation in Step 1) and calculate #x#:

#x = 205 - (-54)#

#x = 259#