How do you solve this set of linear equations: #5x + 10y = 15; 2x + 8y = 10#?

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Answer 1 · 2016-11-27T14:05:57

#x = 1# and #y = 1#

First step is to solve the first equation for #x#:

#5x + 10y - 10y = 15 - 10y#

#5x = 15 - 10y#

(5x)/5 = (15 - 10y)/5#

#x = 3 - 2y#

Next, we substitute #3 - 2y# for #x# in the second equation and solve for#y#:

#2(3 - 2y) + 8y = 10#

#6 - 4y + 8y = 10#

#6 + 4y = 10#

#6 + 4y - 6 = 10 - 6#

#4y = 4#

#(4y)/4 = 4/4#

#y = 1#

Finally, we substitute #1# for #y# in the solution to the first equation and calculate #x#:

#x = 3 - (2*1)#

#x = 3 - 2#

#x = 1#