How do you solve the following system: # 3x – 5y = 53 , 4x+y=10 #?

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Answer 1 · 2017-05-01T13:16:31

See the entire solution process below:

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

#4x + y = 10#

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

#0 + y = -4x + 10#

#y = -4x + 10#

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

#3x - 5y = 53# becomes:

#3x - 5(-4x + 10) = 53#

#3x - (5 * -4x) - (5 * 10) = 53#

#3x - (-20x) - 50 = 53#

#3x + 20x - 50 = 53#

#23x - 50 = 53#

#23x - 50 + color(red)(50) = 53 + color(red)(50)#

#23x - 0 = 103#

#23x = 103#

#(23x)/color(red)(23) = 103/color(red)(23)#

#(color(red)(cancel(color(black)(23)))x)/cancel(color(red)(23)) = 103/23#

#x = 103/23#

Step 3) Substitute #103/23# for #x# in the solution to the second equation at the end of Step 1 and calculate #y#

#y = -4x + 10# becomes:

#y = (-4 * 103/23) + 10#

#y = -412/23 + (10 * 23/23)#

#y = -412/23 + 230/23#

#y = -182/23#

The solution is: #x = 103/23# and #y = -182/23#