Question

3x+y=8________(1) and x²+xy=6________(2) what is Y and what is X simultaneously​

Answer 1

Answer:

(1, 5 ) and (3, - 1 )

Step-by-step explanation:

Given the 2 equations

3x + y = 8 → (1)

x² + xy = 6 → (2)

Rearrange (1) expressing y in terms of x by subtracting 3x from both sides

y = 8 - 3x → (3)

Substitute y = 8 - 3x into (2)

x² + x(8 - 3x) = 6 ← distribute and simplify left side

x² + 8x - 3x² = 6

- 2x² + 8x = 6 ( subtract 6 from both sides )

- 2x² + 8x - 6 = 0 ← divide both sides by - 2

x² - 4x + 3 = 0 ← in standard form

(x - 1)(x - 3) ← in factored form

Equate each factor to zero and solve for x

x - 1 = 0 ⇒ x = 1

x - 3 = 0 ⇒ x = 3

Substitute these values into (3) for corresponding values of y

x = 1 : y = 8 - 3 = 5 ⇒ (1, 5)

x = 3 : y = 8 - 9 = - 1 ⇒ (3, - 1)

Solutions are (1, 5 ) and (3, - 1 )

Answer 2

Answer:

$[3, -1] \\ [1, 5]$

Step-by-step explanation:

{3x + y = 8 >> y = -3x + 8

{x² + xy = 6

${x}^{2} + x[-3x + 8] = 6 \\ {x}^{2} -3{x}^{2} + 8x = 6 \\ -2{x}^{2} + 8x = 6 \\ \\ -2{x}^{2} + 8x - 6 \\ [-2{x}^{2} - 6x] - [2x - 6] \\ \\ -2x[x + 3] - 2[x + 3] \\ \\ -[2x + 2][x + 3] = 0 \\ \\ 1, \: 3 = x$

You plug these back into both equations above to get both y-coordinates of -1 and 5:

$-1, \: 5 = y$

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