SIMULTANEOUS EQUATION ; y+2x=3 and 2x^2-3xy=14

2x^2 - 3xy = 14 .....(1)

y + 2x = 3
y = 3 - 2x ............(2)

Use equation (1) into equation (2);
2x^2 - 3xy = 14
2x^2 - 3x(3 - 2x) = 14
2x^2 - 9x + 6x^2 = 14
8x^2 - 9x - 14 = 0
(8x + 7)(x - 2) = 0
8x + 7 = 0 or x - 2 = 0
x = - 7/8 or x = 2

y = 3 - 2x ...at x = - 7/8, we have;
y = 3 - 2(- 7/8)
y = 3 + 7/4
y = (12 + 7)/4
y = 19/4 ......(- 7/8; 19/4) ......ANSWER!

y = 3 - 2x .....at x = 2, we have;
y = 3 - 2(2)
y = 3 - 4
y = - 1 ......(2; - 1)....ANSWER!

--> y = -2x + 3
=> 2x^2 - 3x ( -2x + 3 ) = 14
= 2x^2 + 6x^2 - 9x = 14
= 8x^2 - 9x - 14 = 0
Delta = 81 + 448 = 529
x = (9 +/- 23 ) / 16 = 2, -7/8
-> y = -4 + 3 = -1
y = -2(-7/8) + 3 = (7/4) + 3 = 19/4

Thus (2, -1) (-7/8, 19/4)

y = - 2*x + 3

2*x^2 - 3*x*( - 2*x + 3) = 14

2*x^2 + 6*x^2 - 9*x - 14 = 0

8*x^2 - 9*x - 14 = 0

(8*x + 7)*(x - 2) = 0

x1 = - 7/8, x2 = 2

y = - 2*x + 3

y1 = - 2*( - 7/8) + 3 = 19/4

y2 = - 2*2 + 3 = - 1

( - 7/8, 19/4), (2, - 1), answer!

2x² - 3(x)(3 - 2x) = 14
2x² - 9x + 6x² = 14
8x² - 9x - 14 = 0
(8x + 7)(x - 2) = 0
x = - 7/8 , x = 2

y = 3 + 7/4 = 19/4
y = 3 - 4 = - 1

Solutions are then:-
(-7/8,19/4) and (2,-1)

y+2x=3---> y = 3-2x , substitute into equation (2) ---> 2x^2-3(3-2x) = 14 , and solve for x , then y

{{x == -7/8, y == 19/4}, {x == 2, y == -1}}

i only know the 1st one, y=1, x=1, so 1+2x1=3

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