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3x +2y +4z = 11
2x -y +3z = 4
5x -3y +5z = -1
I need to know how to solve it

Sagot :

MrRoyal

The solution to the system of equations is x = 1, y = 10 and z = 4

How to solve the system of equations?

The system of equations is given as:

3x +2y +4z = 11

2x -y +3z = 4

5x -3y +5z = -1

Multiply the second equation by 2

So, we have

4x - 2y + 6z = 8

Add this equation to the first equation

3x + 4x + 2y - 2y + 4z + 6z = 11 + 8

Evaluate the like terms

7x + 10z = 19

Multiply the second equation by 3

So, we have

6x - 3y + 9z = 12

Subtract this equation from the third equation

6x - 5x - 3y + 3y + 9z - 5z = 12 + 1

Evaluate the like terms

x + 4z = 13

Make x the subject

x = 13 - 4z

Substitute x = 13 - 4z in 7x + 10z = 19

7(13 - 4z) + 10z = 19

Expand

91 - 28z + 10z = 19

Evaluate the like terms

-18z = -72

Divide

z = 4

Substitute z = 4 in x = 13 - 4z

x = 13 - 4 * 4

Evaluate

x = 1

We have:

2x -y +3z = 4

This gives

2(1) - y + 3 * 4 = 4

Evaluate

2 - y + 12 = 4

This gives

y = 10

Hence, the solution to the system of equations is x = 1, y = 10 and z = 4

Read more about system of equations at

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