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) given equations are x+2y-z = 3 ---> (1)

2x-y+z = 7 ---> (2)

x+3y-z = 4 ---> (3)

To eliminatethe z value add the equations (1)&(2).

x+2y-z = 3

2x-y+z = 7

__________

3x+y = 10 ---> (4)

To eliminate the z value add the equations (2)&(3).

2x-y+z = 7

x+3y-z = 4

__________

3x+2y = 11 ---> (5)

To eliminate the x value Subtract the equations (4) from(5).

3x+2y = 11

3x+y = 10

(-)  (-)   (-)

_________

y = 1

Substitute the y value in (5).

3x+2 = 11

3x = 9

x = 3

Substitute the x,y values in (1).

3+2-z = 3

5-z = 3

-z = -2

z = 2

Solution x = 3, y = 1,z = 2.

 

 

Answer 2

3) 3/4x+4/5y = 5/2

0.75x+0.8y = 2.5 ---> (1)

1/2x-9/10y = -11/2

0.5x-0.9y = -5.5 ---> (2)

Multiple to each side by of equation (1) by 0.5.

0.375x+0.4y = 1.25 ---> (3)

Multiple to each side by of equation (2) by negitive 0.75.

-0.375+0.675y = 4.125 ---> (4)

To eliminate the x value add the equations (4)&(3).

0.375x+0.4y = 1.25

-0.375+0.675y = 4.125

____________________

1.075y = 5.375

Divide to each side by 1.075.

1.075y/1.075 = 5.375/1.075

y = 5

Substitute the y value in (1).

0.75x+4 = 2.5

0.75x = -1.5

Divide to each side by 0.75.

x = -2

Solution x = -2, y = 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 is x = 0, y = 2,and z = 0.