How do you solve the simultaneous equations #y = 3x# and # x + 2y =21#?

1 Answer
Alan P.
Jul 13, 2015

Since we are given an expression for #y# as one of the equations, the simplest way to solve this pair of equations is through substitution.
#(x,y) = (3,9)#

Explanation:

[1]#color(white)("XXXX")##y=3x#
[2]#color(white)("XXXX")##x+2y = 21#

Based on [1], we can replace #y# with #3x# in [2], giving
[3]#color(white)("XXXX")##x+2(3x) = 21#
Simplifying:
[4]#color(white)("XXXX")##7x = 21#
or
[5]#color(white)("XXXX")##x=3#

Based on [5], we can replace #x# with #3# in [1], giving
[6]#color(white)("XXXX")##y = 3(3)#
or
[7]#color(white)("XXXX")##y= 9#

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