How do you solve the system #4c+2d=10# and #c+3d=10# by substitution?

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Answer 1 · 2015-05-27T13:31:40

Given
#"[1] " 4c+2d = 10#
#"[2] " c+3d = 10#

[1] can be re-expressed as
#"[3] "d = 5-2c#

then [3] can be substituted into [2]
#"[4] "c+3(5-2c) = 10#

Simplifying

#-5c +15 = 10#
or
#"[5] "c=1#

Substituting [5] back into [2]

#1+3d =10#
or
#"[6] "d=3#

The solution is #(c,d) = (1,4)#