Question

What is the solution of the system of equations?

3 x + 2 y + z = 7
5 x + 5 y + 4 z = 3
3 x + 2 y + 3 z = 1

Answer 1

The answer to your question is:

x = 4

y = -1

z = -3

Explanation:

3 x + 2 y + z = 7

5 x + 5 y + 4 z = 3

3 x + 2 y + 3 z = 1

`\left[\begin{array}{ccc}3&2&1\\5&5&4\\3&2&3\end{array}\right]`

= 45 + 10 + 24 - (30 + 24 + 15)

= 79 - 69

Δ = 10

`\left[\begin{array}{ccc}7&2&1\\3&5&4\\1&2&3\end{array}\right]`

= 105 + 6 + 8 - (18 + 56 + 5)

= 119 - 79

Δx = 40

`\left[\begin{array}{ccc}3&7&1\\5&3&4\\3&1&3\end{array}\right]`

= 27 + 5 + 84 - ( 105 + 12 + 9)

= 116 - 126

Δy = -10

`\left[\begin{array}{ccc}3&2&7\\5&5&3\\3&2&1\end{array}\right]`

= 15 + 70 + 18 - (10 + 18 + 105)

= 103 - 133

= -30

Δz = -30

x = Δx /Δ = 40/10 = 4

y = Δy/Δ = -10/10 = -1

z = Δz/Δ = -30/10 = -3

Answer 2

x = 4, y = -1 and z = -3.

Explanation:

3 x + 2 y + z = 7 (A)

5 x + 5 y + 4 z = 3 (B)

3 x + 2 y + 3 z = 1 (C)

Subtract: A - C:

-2z = 6

z = -3.

Substitute for z in equations A and B:

3 x + 2 y - 3 = 7

3 x + 2 y = 10 (D)

5x + 5y = 15 (E)

Multiply D by -5 and E by 2:

-15x - 10y = -50

10x + 10y = 30 Adding these 2 equations:

-5x = -20

x = 4.

Finally Substitute x = 4 and z = -3 in equation C:

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

2y = 1 - 12 + 9 = -2

y = -1.