Question

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Solve the system of equations using determinants.
x + y - z = 4

3x + 4y - 3z = 16

9x - 3y + 4z = 14
Find the values of determinants D, Dx,Dy and Dz

Answer 1

Answer:
`(x,y,z) \rightarrow (2,4,2)`

Explanation:

Eliminate one of the variables.

`\textrm{EQ1: } x+y-z=4\\EQ2: 3x+4y-3z=16\\\\\text{Multiply EQ1 times negative 3}\\\\EQ1 \cdot -3: -3x-3y+3z=-12\\\text{EQ2: } 3x+4y-3z=16\\`

Solve by elimination.

`y = 4`

Substitute y=4 into EQ1.

`x+4-z=4\\x-z=0\\x=z`

Substitute y=4 and x=z into EQ2.

`9x-3y+4z=14\\9x-3(4)+4x=14\\13x-12=14\\13x=26\\x=2`

z=x=2

Solution:
`(x,y,z) \rightarrow (2,4,2)`