Question

28x + 4y - z = 32 x + 3y + 10z = 24 2x + 17y + 4z = 35

Answer 1

Answer:

1] 28x + 4y - z = 32

[2] 2x + 17y + 4z = 35

[3] x + 3y + 10z = 24

Solve by Substitution :

// Solve equation [3] for the variable x

[3] x = -3y - 10z + 24

// Plug this in for variable x in equation [1]

[1] 28•(-3y-10z+24) + 4y - z = 32

[1] - 80y - 281z = -640

// Plug this in for variable x in equation [2]

[2] 2•(-3y-10z+24) + 17y + 4z = 35

[2] 11y - 16z = -13

// Solve equation [2] for the variable y

[2] 11y = 16z - 13

[2] y = 16z/11 - 13/11

// Plug this in for variable y in equation [1]

[1] - 80•(16z/11-13/11) - 281z = -640

[1] - 4371z/11 = -8080/11

[1] - 4371z = -8080

// Solve equation [1] for the variable z

[1] 4371z = 8080

[1] z = 8080/4371

// By now we know this much :

x = -3y-10z+24

y = 16z/11-13/11

z = 8080/4371

// Use the z value to solve for y

y = (16/11)(8080/4371)-13/11 = 6587/4371

// Use the y and z values to solve for x

x = -3(6587/4371)-10(8080/4371)+24 = 4343/4371

Answer 2

Answer:

Solution is ${x,y,z} = {4343/4371,6587/4371,8080/4371}$

Step-by-step explanation:

System of Linear Equations entered :

 $[1] 28x + 4y - z = 32$

 $[2] x + 3y + 10z = 24$

$[3] 2x + 17y + 4z = 35$

Solve by Substitution :

// Solve equation [2] for the variable  x

$[2] x = -3y - 10z + 24$

// Plug this in for variable  x  in equation [1]

 $[1] 28*(-3y-10z+24) + 4y - z = 32\\ [1] - 80y - 281z = -640$

// Plug this in for variable  x  in equation [3]

$[3] 2*(-3y-10z+24) + 17y + 4z = 35\\ [3] 11y - 16z = -13$

// Solve equation [3] for the variable  y

$[3] 11y = 16z - 13\\ [3] y = 16z/11 - 13/11$

// Plug this in for variable  y  in equation [1]

 $[1] - 80*(16z/11-13/11) - 281z = -640\\ [1] - 4371z/11 = -8080/11\\ [1] - 4371z = -8080$

// Solve equation [1] for the variable  z

 $[1] 4371z = 8080 \\ [1] z =\frac{8080}{4371}$

/ By now we know this much :

  $x = -3y-10z+24\\ y = 16z/11-13/11\\ z = 8080/4371$

// Use the  z  value to solve for  y

  $y = (16/11)(8080/4371)-13/11 = 6587/4371$

// Use the  y  and  z  values to solve for  x

$x = -3(6587/4371)-10(8080/4371)+24 = 4343/4371$

Solution :

${x,y,z} = {4343/4371,6587/4371,8080/4371}$