Question

help? =)
2x+2y-z=9
3x+3y+z=16
x-2y=-1

Answer 1

well the easy this to do is to rewrite the last equation as

x = 2y - 1

and then substitute it into the first 2 equations

2(2y - 1) + 2y - z = 9

and

3(2y - 1) + 3y + z = 16


so your 2 equations are

6y - z = 11
9y + z = 19

you now have 2 equations and 2 unknowns.

next step is to eliminate another letter, z is the easiest

add the equations together

15y = 30

so y = 2

you just now need to backtrack and find z and then x

Answer 2

thank you!! =)

Answer 3

For systems bigger than two equations and two unknowns, it's better to use matrices. Do you know linear algebra?

Answer 4

matrices? yeah

Answer 5

This system can be represented in matrix form by\[\begin{bmatrix}
2 & 2 & -1\\
3 & 3 & 1\\
1 & -2 & 0
\end{bmatrix}\begin{bmatrix}
x\\
y\\
z
\end{bmatrix}=\begin{bmatrix}
9\\
16\\
1
\end{bmatrix}.\]All you need to do is find the largest matrix's inverse, and you must know the rest from there.

Answer 6

i had trouble starting off the equations but yall helped so much, thanks