Question

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

Answer 1

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

Explanation:

Given:

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

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

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`color(blue)("Expressing "x" in terms of "t)`

From Equation(1)

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

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`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")`