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

Dec 7, 2016

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

#### Explanation:

Given:

$- 7 x - 7 t = 14 \text{ } \ldots \ldots \ldots \ldots \ldots . . E q u a t i o n \left(1\right)$

$y = 3 x + 2 \text{ } \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots . E q u a t i o n \left(2\right)$

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$\textcolor{b l u e}{\text{Expressing "x" in terms of } t}$

From Equation(1)

$\textcolor{b l u e}{x = - t + 2} \ldots \ldots \ldots \ldots \ldots . . E q u a t i o n \left({1}_{a}\right)$

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
$\textcolor{b l u e}{\text{Expressing "y" in terms of } t}$

Substitute for $x$ in equation(2) using equation$\left({1}_{a}\right)$

$y = 3 \left(- t + 2\right) + 2$

$\textcolor{b l u e}{y = - 3 t + 8}$

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

$\textcolor{red}{\text{ 3 variables implies 3d graph}}$