How do you solve the system #-7x-7t=14, y=3x+2# using substitution?

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Answer 1 · 2016-12-07T10:57:20

You have 3 unknowns but only 2 equations. So you can not determine actual values. Only relationships.

Given:

#-7x-7t=14" ".................Equation(1)#

#y=3x+2" ".........................Equation(2)#

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#color(blue)("Expressing "x" in terms of "t)#

From Equation(1)

#color(blue)(x=-t+2).................Equation(1_a)#

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#color(blue)("Expressing "y" in terms of "t)#

Substitute for #x# in equation(2) using equation#(1_a)#

#y=3(-t+2)+2#

#color(blue)(y=-3t+8)#

Graph#" "color(red)(->" read t where there is a z on the graph")#

#color(red)(" 3 variables implies 3d graph")#
Tony B