Question

Solve the simultaneous equation 2x+y=22 =12, x + 24+2 = 18, 2x -y +22=16 ​

Answer 1

The solution for the simultaneous equations 2x + y - 2z = 12, x + 2y +z =18 and 2x - y + 2z =16 are x = 7, y = 4 and z = 3

What are linear equations?

Linear equations are equations that have constant average rates of change, slope or gradient

How to determine the solution to the simultaneous equations?

A system of linear equations is a collection of at least two linear equations.

In this case, the system of equations is given as

2x + y - 2z = 12,

x + 2y +z =18

2x - y + 2z =16

Eliminate y and z in the equations by adding the first and the third equation together

This gives

2x + y - 2z = 12,

+

2x - y + 2z =16

--------------------------

4x = 28

Divide both sides by 4

x = 7

Substitute x = 7 in x + 2y +z =18 and 2x - y + 2z =16

7 + 2y +z =18

2(7) - y + 2z =16

This gives

2y + z = 11

-y + 2z= 2

Multiply -y + 2z= 2 by 2

-2y + 4z= 4

Add -2y + 4z= 4 and 2y + z = 11

5z = 15

Divide by 5

z = 3

Substitute z = 3 in -y + 2z= 2

-y + 2*3= 2

Evaluate

y = 4

Hence, the solution for the simultaneous equations 2x + y - 2z = 12, x + 2y +z =18 and 2x - y + 2z =16 are x = 7, y = 4 and z = 3

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