Solve 3 problems using the addition method?

Question

Solve using the addition method: 

1.) 

3x − 2y + 3z = -4 
2x + y − 3z = 2 
3x + 4y + 5z = 8 

2.) 

x + 2y − z = 3 
2x − y + z = 7 
x + 3y − z = 4 

3.) 

3/4x + 4/5y = 5/2 
1/2x - 9/10y = -11/2 


Any help would be awesome thanks!!!

Answer 1

(2).

The system of equations are .

Use the elimination method to make a system of two equations in two variables.

The two equations 1 and 2 contains opposite coefficient of z - variable.

Write the equations 1 and 2 in column form and add the corresponding columns to eliminate z - variable.

The resultant equation is taken as fourth equation : 3x + y = 10.

The two equations 2 and 3 contains same coefficient of z - variable.

Write the equations 2 and 3 in column form and subtract the corresponding columns to eliminate z - variable.

The resultant equation is taken as fifth equation : 3x + 2y = 11.

Solve the system of two equations with two variables.

The two equations 4 and 5 contains same coefficient of x - variable.

Write the equations 4 and 5 in column form and subtract the corresponding columns to eliminate x - variable.

.

The resultant equation is - y = - 1 ----> y = 1.

Use one of the equation with two variables (Equation: 4 or 5) to solve for x.

The fourth equation: 3x + y = 10.

3x + (1) = 10

3x = 9

x = 3.

Solve for z using one of the original equations with three variables.

The second equation: 2x - y + z = 7.

2(3) - (1) + z = 7

5 + z = 7

z = 2.

The solution (x, y, z) = (3, 1, 2).

Answer 2

(3).

The system of equations are (3/4)x + (4/5)y = 5/2 and (1/2)x - (9/10)y = - 11/2.

Equation 1 : (3/4)x + (4/5)y = 5/2       ⇒    0.75x + 0.8y = 2.5.

Equation 2 : (1/2)x - (9/10)y = - 11/2  ⇒    0.5x - 0.9y = - 5.5.

Neither variable has a common coefficient.The coefficient  of the y - variables are 0.8 and 0.9 and their least common multiple is 0.72, so multiply each equation by the value  that will make the y - coefficient 0.72.

To get two equations that contain opposite terms multiply the first equation by 0.9 and multiply the second equation by 0.8.

Write the equations in column form and add the corresponding columns to eliminate y - variable.

The resultant equation is 1.075x = - 2.15 ⇒ x = - 2.

Substitute the value of ⇒ x = - 2 in either of the original equations and solve for y.

The second equation : 0.5x - 0.9y = - 5.5.

0.5(- 2) - 0.9y = - 5.5

- 1 - 0.9y = - 5.5

- 0.9y = - 4.5

y = 5.

The solution (x, y) = (-2, 5).

Answer 3

(1).

Elimination method (Addition method) :

The system of equations are .

Use the elimination method to make a system of two equations in two variables.

The two equations 1 and 2 contains opposite coefficient of z - variable.

Write the equations 2 and 3 in column form and add the corresponding columns to eliminate z - variable.

The resultant equation is taken as fourth equation : .

 

To get two equations 2 and 3 that contain opposite terms multiply the second equation by 5 and multiply the third equation by 3.

Write the equations in column form and add the corresponding columns to eliminate z - variable.

The resultant equation is taken as fifth equation : .

 

Solve the system of two equations with two variables.

Neither variable has a common coefficient in equation 4 and 5.The coefficient  of the y - variables are -1 and 17 and their least common multiple is -17, so multiply each equation by the value  that will make the y - coefficient -17.

To get two equations 4 and 5 that contain opposite terms multiply the fourth equation by 17.

Write the equations in column form and add the corresponding columns to eliminate y - variable.

The resultant equation is : .

 

Use one of the equation with two variables (Equation : 4 or 5) to solve for y.

The fourth equation : .

.

 

Solve for z using one of the original equations with three variables.

The third equation: .

.

The solution x = 0, y = 2,and z = 0.