Solve each system of equations (systems with 3 variables)

9x + 3y - 4z = 37
4x + 3y +7z = 16
x - 5y + 8z = -31

my answer is (2,5,-1)
is that right?

x = 2 , y = 5 , z = -1 You are correct!!!

Step-by-step explanation:

Solve the following system:

{9 x + 3 y - 4 z = 37 | (equation 1)

4 x + 3 y + 7 z = 16 | (equation 2)

x - 5 y + 8 z = -31 | (equation 3)

Subtract 4/9 × (equation 1) from equation 2:

{9 x + 3 y - 4 z = 37 | (equation 1)

0 x+(5 y)/3 + (79 z)/9 = (-4)/9 | (equation 2)

x - 5 y + 8 z = -31 | (equation 3)

Multiply equation 2 by 9:

{9 x + 3 y - 4 z = 37 | (equation 1)

0 x+15 y + 79 z = -4 | (equation 2)

x - 5 y + 8 z = -31 | (equation 3)

Subtract 1/9 × (equation 1) from equation 3:

{9 x + 3 y - 4 z = 37 | (equation 1)

0 x+15 y + 79 z = -4 | (equation 2)

0 x - (16 y)/3 + (76 z)/9 = (-316)/9 | (equation 3)

Multiply equation 3 by 9/4:

{9 x + 3 y - 4 z = 37 | (equation 1)

0 x+15 y + 79 z = -4 | (equation 2)

0 x - 12 y + 19 z = -79 | (equation 3)

Add 4/5 × (equation 2) to equation 3:

{9 x + 3 y - 4 z = 37 | (equation 1)

0 x+15 y + 79 z = -4 | (equation 2)

0 x+0 y+(411 z)/5 = (-411)/5 | (equation 3)

Multiply equation 3 by 5/411:

{9 x + 3 y - 4 z = 37 | (equation 1)

0 x+15 y + 79 z = -4 | (equation 2)

0 x+0 y+z = -1 | (equation 3)

Subtract 79 × (equation 3) from equation 2:

{9 x + 3 y - 4 z = 37 | (equation 1)

0 x+15 y+0 z = 75 | (equation 2)

0 x+0 y+z = -1 | (equation 3)

Divide equation 2 by 15:

{9 x + 3 y - 4 z = 37 | (equation 1)

0 x+y+0 z = 5 | (equation 2)

0 x+0 y+z = -1 | (equation 3)

Subtract 3 × (equation 2) from equation 1:

{9 x + 0 y - 4 z = 22 | (equation 1)

0 x+y+0 z = 5 | (equation 2)

0 x+0 y+z = -1 | (equation 3)

Add 4 × (equation 3) to equation 1:

{9 x+0 y+0 z = 18 | (equation 1)

0 x+y+0 z = 5 | (equation 2)

0 x+0 y+z = -1 | (equation 3)

Divide equation 1 by 9:

{x+0 y+0 z = 2 | (equation 1)

0 x+y+0 z = 5 | (equation 2)

0 x+0 y+z = -1 | (equation 3)

Collect results:

 {x = 2 , y = 5 , z = -1

the size of the resulting matrix is 1-by-3.

step-by-step explanation:

the size of the two matrices given are as follows:

no .of rows of matrix 1 = 1

no .of columns of matrix 1 = 3

no .of rows of matrix 1 = 3

no .of columns of matrix 1 = 3

to find the size of the resulting matrix without actually solving the multiplication of the matrix, this is what you do:

if resulting matrix = matrix 1 * matrix 2

no. of rows of the resulting matrix = number of rows of matrix 1

no. of columns of resulting matrix = number of columns of matrix 2

note: the order of the matrices matter!