How do you solve this system of equations: #x+ 4y = 5; 4x - 2y = 11#?

Question

1759 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-11-16T14:11:31

#y = 1/2# or #0.5# and #x = 3#

Step 1) Solve the first equation for #x# while keeping the equation balanced:

#x + 4y - 4y = 5 - 4y#

#x = 5 - 4y#

Step 2)

Substitute #5 - 4y# for #x# in the second equation and solve for #y# while keeping the equation balanced:

#4(5 - 4y) - 2y = 11#

#20 - 16y - 2y = 11#

#20 - 18y = 11#

#20 - 18y - 20 = 11 - 20#

#-18y = -9#

#-18y/-18 = -9/-18#

#y = 1/2# or #0.5#

Step 3) Substitute #1/2# for #y# in the first equation and solve for #x# while keeping the equation balanced:

#x + 4 1/2 = 5#

#x + 2 = 5#

#x + 2 - 2 = 5 - 2#

#x = 3#