How do you solve the system of equations #2x + 5y = 3# and #2y + x = 3#?

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Answer 1 · 2018-06-02T13:42:24

See a solution process below:

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

#2y + x = 3#

#2y - color(red)(2y) + x = 3 - color(red)(2y)#

#0 + x = 3 - 2y#

#x = 3 - 2y#

Step 2) Substitute #(3 -2y)# for #x# in the first equation and solve for #y#:

#2x + 5y = 3# becomes:

#2(3 -2y) + 5y = 3#

#(2 * 3) - (2 * 2y) + 5y = 3#

#6 - 4y + 5y = 3#

#6 + (-4 + 5)y = 3#

#6 + 1y = 3#

#6 + y = 3#

#6 - color(red)(6) + y = 3 - color(red)(6)#

#0 + y = -3#

#y = -3#

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

#x = 3 - 2y# becomes:

#x = 3 - (2 * -3)#

#x = 3 - (-6)#

#x = 3 + 6#

#x = 9#

The Solution Is:

#x = 9# and #y = -3#

Or

#(9, -3)#