Question

Use the substitution method to solve the following system of equations.
4x - y - 3z = -3
x - 2y - 2z = -3
x + y + 3z = -2

Answer 1

Substitution for 3 equations?? Hmm interesting :o
Ok there are many different ways we could do this.
let's try this. Using the third equation, let's solve for y.\[\large x+y+3z=-2 \qquad \qquad \rightarrow \qquad \qquad \color{royalblue}{y=-2-x-3z}\]

Then let's plug our new `y` into one of the other equations. How bout the first one?\[\large 4x-\color{royalblue}{y}-3z=-3 \qquad \rightarrow \qquad 4x-(\color{royalblue}{-2-x-3z})-3z=-3\]

Confused about any of that yet?
We solved for y in one equation, and replaced that y in another equation with its equivalent in x and z.

We now have an equation with 2 variables, not 3.

Answer 2

(-1, 2, -1)
(1, -2, 1)
(-1, -2, 1)
(1, -2, -1)
These are the answers

Answer 3

lol