Question

Solve the system of equations.

2x + 2y + 3z = 4
5x + 3y + 5z =
3x + 4y + 6z = 5
a. (x = 2, y = 21, z = -13)
b. (x = 3, y = 20,2 = -14)
c. (x = 5, y = 18, z =-12)
d. (x = 4, y = 19,2 =-15)

Answer 1

Option b. (x = 3, y = 20, z = -14)

Explanation:

Given:

2x + 2y + 3z = 4

5x + 3y + 5z = 5

3x + 4y + 6z = 5

Solve using Cramer’s rule

∴
`\left[\begin{array}{ccc}2&2&3\\5&3&5\\3&4&6\end{array}\right] =\left[\begin{array}{ccc}4\\5\\5\end{array}\right]`

∴A =
`\left[\begin{array}{ccc}2&2&3\\5&3&5\\3&4&6\end{array}\right] = -1`

Ax =
`\left[\begin{array}{ccc}4&2&3\\5&3&5\\5&4&6\end{array}\right] = -3`

Ay =
`\left[\begin{array}{ccc}2&4&3\\5&5&5\\3&5&6\end{array}\right] =-20\\`

Az =
`\left[\begin{array}{ccc}2&2&4\\5&3&5\\3&4&5\end{array}\right] = 14`

∴ x = Ax/A = -3/-1 = 3

y = Ay/A = -20/-1 = 20

z = Az/A = 14/-1 = -14

So, the answer is option b. (x = 3, y = 20, z = -14)