How do you solve the following system: # 3x+5y=5 , 4x+y=10 #?

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Answer 1 · 2017-01-23T14:48:48

See the entire solution process below:

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

#4x + y - color(red)(4x) = 10 - color(red)(4x)#

#4x - color(red)(4x) + y = 10 - color(red)(4x)#

#0 + y = 10 - 4x#

#y = 10 - 4x#

Step 2) Substitute #color(red)(10 - 4x)# for #y# in the first equation and solve for #x#:

#3x + 5(10 - 4x) = 5#

#3x + 50 - 20x = 5#

#3x - 20x + 50 = 5#

#-17x + 50 = 5#

#-17x + 50 + color(red)(17x) - color(blue)(5) = 5 + color(red)(17x) - color(blue)(5)#

#-17x + color(red)(17x) + 50 - color(blue)(5) = 5 - color(blue)(5) + color(red)(17x)#

#0 + 50 - 5 = 0 + 17x#

#45 = 17x#

#45/color(red)(17) = (17x)/color(red)(17)#

#45/17 = (color(red)(cancel(color(black)(17)))x)/cancel(color(red)(17))#

#45/17 = x#

#x = 45/17#

Step 3) Substitute #color(red)(45/17)# for #x# in the solution to the second equation at the end of Step 1:

#y = 10 - (4 xx 45/17)#

#y = (17/17 xx 10) - (180/17)#

#y = 170/17 - 180/17#

#y = -10/17#

The solution is: #x = 45/17#, #y = -10/17# or #(45/17, -10/17)#