How do you solve linear combinations like #x+y=5# and #2x+y=6#?

1 Answer
May 24, 2018

Answer:

See a solution process below:

Explanation:

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

#x + y = 5#

#x + y - color(red)(y) = 5 - color(red)(y)#

#x + 0 = 5 - y#

#x = 5 - y#

Step 2) Substitute #(5 - y)# for #x# in the second equation and solve for #y#:

#2x + y = 6# becomes:

#2(5 - y) + y = 6#

#(2 * 5) - (2 * y) + y = 6#

#10 - 2y + y = 6#

#10 - 2y + 1y = 6#

#10 + (-2 + 1)y = 6#

#10 + (-1)y = 6#

#10 - 1y = 6#

#10 - y = 6#

#10 - color(red)(6) - y + color(blue)(y) = 6 - color(red)(6) + color(blue)(y)#

#4 - 0 = 0 + y#

#4 = y#

#y = 4#

Step 3) Substitute #4# for #y# in the solution to the first equation at the end of Step 1 and calculate #x#:

#x = 5 - y# becomes:

#x = 5 - 4#

#x = 1#

The Solution Is:

#x = 1# and #y = 4#

Or

#(1, 4)#