A system of equations is shown. What is the solution to the system? 4c+2d=11 (7/2)d=41-22c

1 Answer
Apr 18, 2018

#c=29/20#
#d=13/5#

Explanation:

I'll start with #4c+2d=11#. Because #d# looks easier in #(7/2)*d=41-22c#, I'll solve for #d#.
#4c+2d=11# Isolate #d# and coefficients on one side:
#2d=11-4c# Isolate #d#:
#d=(11/2)-2c#

Now that we have #d# in terms of #c# we can input it into the other equation:
#(7/2)*((11/2)-2c)=41-22c# Distribute:
#(77/4)-7c=41-22c# Isolate #c# and coefficients on one side:
#15c=87/4# Isolate #c#:
#c=29/20#

We can input this into the first equation to find #d#:
#4(29/20)+2d=11# Combine like terms:
#29/5+2d=11# Isolate #d# and its coefficients on one side:
#2d=26/5#
#d=13/5#