Question

Solve equations: x + 2y = 13, x + y + z = 12, 2y + z = 11​

Answer 1

Answer:

Step-by-step explanation:

Value of x=5, y=4,z=3

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Answer 2

Answer:

Value of x is 5, value of y is 4 and value of z is 3.

Step-by-step explanation:

Given three equations are

$x + 2y = 13.....(1) \\ x + y + z = 12.....(2) \\ 2y + z = 11......(3)$

We are adding equation (1) and (2),

$x + 2y + 2y + z = 13 + 11 \\ x + 4y + z = 24.......(5)$

We are subtracting equation (2) from equation (5),

$x + 4y + z - (x + y + z) = 24 - 12 \\ x + 4y + z - x - y - z = 12 \\ 4y - y = 12 \\ 3y = 12 \\ y = \frac{12}{3} \\ y = 4$

We are putting value of y in equation (1),

$x + 2 \times 4 = 13 \\ x = 13 - 8 \\ x = 5$

We are putting value of x and y in equation (2),

$5 + 4 + z = 12 \\ 9 + z = 12 \\ z = 12 - 9 \\ z = 3$

This is a problem of Algebra.

Some important Algebra formulas:

(a + b)² = a² + 2ab + b²

(a − b)² = a² − 2ab − b²

(a + b)³ = a³ + 3a²b + 3ab² + b³

(a - b)³ = a³ - 3a²b + 3ab² - b³

a³ + b³ = (a + b)³ − 3ab(a + b)

a³ - b³ = (a -b)³ + 3ab(a - b)

a² − b² = (a + b)(a − b)

a² + b² = (a + b)² − 2ab

a² + b² = (a − b)² + 2ab

a³ − b³ = (a − b)(a² + ab + b²)

a³ + b³ = (a + b)(a² − ab + b²)

Know more about Algebra,

1) https://brainly.in/question/13024124

2) https://brainly.in/question/1169549