How do you find the solution of the system of equations #4x - 5y = 40 # and #2x + 10y=20#?

2 Answers
Jun 16, 2018

Answer:

See a solution process below:

Explanation:

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

#2x + 10y = 20#

#2x + 10y - color(red)(10y) = 20 - color(red)(10y)#

#2x + 0 = 20 - 10y#

#2x = 20 - 10y#

#(2x)/color(red)(2) = (20 - 10y)/color(red)(2)#

#x = 20/color(red)(2) - (10y)/color(red)(2)#

#x = 10 - 5y#

Step 3) Substitute #(10 - 5y)# for #x# in the first equation and solve for #y#:

#4x - 5y = 40# becomes:

#4(10 - 5y) - 5y = 40#

#(4 xx 10) - (4 xx 5y) - 5y = 40#

#40 - 20y - 5y = 40#

#40 + (-20 - 5)y = 40#

#40 + (-25)y = 40#

#40 - 25y = 40#

#40 - color(red)(40) - 25y = 40 - color(red)(40)#

#0 - 25y = 0#

#-25y = 0#

#(-25y)/color(red)(-25) = 0/color(red)(-25)#

#y = 0#

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

#x = 10 - 5y# becomes:

#x = 10 - (5 xx 0)#

#x = 10 - 0#

#x = 10#

The Solution Is:

#x = 10# and #y = 0#

Or

#(10, 0)#

Here's the solution graphically:

#graph{(4x-5y-40)(2x+10y-20)=0[-5,15,-5,5]}