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:
[tex][3, -1] \\ [1, 5][/tex]
Step-by-step explanation:
{3x + y = 8 >> y = -3x + 8
{x² + xy = 6
[tex]{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[/tex]
You plug these back into both equations above to get both y-coordinates of -1 and 5:
[tex]-1, \: 5 = y[/tex]
I am joyous to assist you anytime.
