SOLUTION: Find the values of the variables in the matrices: -3 * 2 x + 2 -1 = -4 z 3x 4y 4 -3 22 14 I couldn't put the bracket around each matrice

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Question 1193741: Find the values of the variables in the matrices:
-3 * 2 x + 2 -1 = -4 z
3x 4y 4 -3 22 14
I couldn't put the bracket around each matrice. The 3 is multiplied by the first matrix.
Thanks



Answer by math_tutor2020(3817) About Me  (Show Source):
You can put this solution on YOUR website!

The -3 out front the first matrix tells us to multiply -3 by everything inside just that particular matrix.
This means
Eg: The 2 turns into -3(2) = -6 in the upper left corner.

So we go from this given equation

to this


For now, focus on the lower left corner of each given matrix.
Those bottom left corner entries are:
-9x, 4, and 22

The first two lower left corner entries add up to the third entry. Meaning we have the equation -9x+4 = 22
Effectively, each corner is treated separately to form a different equation.
Or you can think of it like this template here

and the lower left corner would yield c+g = k

Solve for x:
-9x+4 = 22
-9x = 22-4
-9x = 18
x = 18/(-9)
x = -2

Now apply substitution to go from this

to this

The -3x becomes 6 since -3x = -3(-2) = 6
The -9x becomes 18 since -9x = -9(-2) = 18
Everything else remains the same

Next, focus on the bottom righthand corners of each matrix.
The elements in those corners are: -12y, -3, 14
They produce the equation shown below in which we solve for y

-12y+(-3) = 14
-12y-3 = 14
-12y = 14+3
-12y = 17
y = 17/(-12)
y = -17/12
We could get an approximation here (roughly -17/12 = -1.41667), but I think it's better to keep it as a fraction.

Lastly, focus on the upper righthand corners to determine z
6+(-1) = z
6-1 = z
z = 5


Answers:
x = -2
y = -17/12
z = 5