7條解方程................

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(1)

2x^2 + 3x + 6 = 5y --- (1)
2x - 10y + 11 = 0 --- (2)

From (2) :

x = (10y-11)/2 --- (3)

Sub (3) into (1) :

2[(10y-11)/2]^2 + 3(10y-11)/2 + 6 = 5y
50y^2 - 100y + 50 = 0
50(y^2-2y+1) = 0
50(y-1)^2 = 0
y = 1 --- (4)

Sub (4) into (3) :

x = [10(1)-11]/2
= -1/2

Answer : x = -1/2, y = 1.

(2)

2x^2 - 3x - y = 10 --- (1)
5x + 3y = 2 --- (2)

From (2) :

y = (2-5x)/3 --- (3)

Sub (3) into (1) :

2x^2 - 3x - (2-5x)/3 = 0
3x^2 - 2x - 1 = 0
(3x+1)(x-1) = 0
x = -1/3 or 1

When x = -1/3,

y = [2-5(-1/3)]/3
= 11/9

When x = 1,

y = [2-5(1)]/3
= -1

Answer : x = -1/3, y = 11/9; x = 1, y = -1.

(3)

x^2 - 4x - 2y = 9 --- (1)
2x - y = 3 --- (2)

From (2) :

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

Sub (3) into (1):

x^2 - 4x - 2(2x-3) = 9
x^2 - 8x - 3 = 0
x = 4 ± √19

When x = 4 + √19,

y = 2(4+√19) - 3
= 5 + 2√19

When x = 4 - √19,

y = 2(4-√19) - 3
= 5 - 2√19

Answer : x = 4+√19, y = 5+2√19; x = 4-√19, y = 5-2√19.

(4)

x^2 + 2x + 1 = 3y --- (1)
3x - 2y + 3 = 0 --- (2)

From (2):

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

Sub (3) into (1) :

x^2 + 2x + 1 = (3x+3)/2
2x^2 + x - 1 = 0
(2x-1)(x+1) = 0
x = -1 or 1/2

When x = -1,

y = [3(-1)-3]/2
= -3

When x = 1/2,

y = [3(1/2)-3]/2
= 3/4

Answer : x = -1, y = -3; x = 1/2, y = 3/4.

(5)

2y = -x^2 + 2x + 13 --- (1)
5x + y = 0 --- (2)

From (2) :

y = -5x --- (3)

Sub (3) into (1) :

2(-5x) = -x^2 + 2x + 13
x^2 - 12x - 13 = 0
(x-13)(x+1) = 0
x = -1 or 13

When x = -1

y = -5(-1)
= 5

When x = 13

y = -5(13)
= -65

Answer : x = -1, y = 5; x = 13, y = -65.

(6)

x^2 + y^2 + 4x - 12 = 0 --- (1)
x - y + 6 = 0 --- (2)

From (2) :

y = x + 6 --- (3)

Sub (3) into (1)

x^2 + (x+6)^2 + 4x - 12 = 0
2x^2 + 16x + 24 = 0
2(x+2)(x+6) = 0
x = -6 or -2

When x = -6,

y = -6 + 6
= 0

When x = -2,

y = -2 + 6
= 4

Answer : x = -6, y = 0; x = -2, y = 4.

(7)


x^2 + y^2 + 6x - 8y = 0 --- (1)
x + 3y - 14 = 0 --- (2)

From (2) :

x = 14 - 3y --- (3)

Sub (13) into (1) :

(14-3y)^2 + y^2 + 6(14-3y) - 8y = 0
10y^2 - 110y + 280 = 0
10(y-7)(y-4) = 0
y = 4 or 7

When y = 4,

x = 14 - 3(4)
= 2

When y = 7,

x = 14 - 3(7)
= -7

Answer : x = 2, y = 4; x = -7, y = 7.

(1)
2x^2+3x+6=5y i
2x-10y+11=0 ii
由i,(2x^2+3x+6)/5=y iii
2x-10[(2x^2+3x+6)/5]+110
2x-4x^2-6x-12+11=0
-4x^2-4x-1=0
x=-0.5
代x=-0.5入iii
y=[2(-0.5)^2+3(-0.5)+6]/5
y=1
(x,y)=(-0.5,1)

(2)
2x^2-3x-y=10 i
5x+3y=2 ii
由i, 2x^2-3x-10=y iii
代iii入ii
5x+3(2x^2-3x-10)=2
5x+6x^2-9x-30-2=0
6x^2-4x-32=0
x=8/3 和x=-2
代x=8/3入i
5(8/3)+3y=2
y=-34/9
代x=-2入ii
5(-2)+3y=2
y=4
(x,y)=(8/3,-34/9) 和 (x,y)=(-2,4)

(3)
x^2-4x-2y=9 i
2x-y=3 ii
由ii, 2x-3=y iii
代iii入i
x^2-4x-2(2x-3)=9
x^2-4x-4x+6-9=0
x^2-8x-3=0
x= 4 ± √19
代4+√19入iii
2(4+ √19)-3=y
y=8+2√19-3
y=5+2√19
代x=4-√19入iii
y=8-2√19-3
y=5-2√19
(x,y)=(4+√19 , 5+2√19) 和 (x,y)=(4-√19 , 5+2√19)

(4)
x^2+2x+1=3y i
3x-2y+3=0 ii
由i,y=(x^2+2x+1)/3 iii
代iii入ii
3x-2[(x^2+2x+1)/3]+3=0
3x-(2x^2+4x+2)/3+3=0
(-2x^2)/3+(5x)/3+7/3=0
-2x^2+5x+7=0
x=-1 和 x=3.5
代x=-1入iii
y=[(-1+1)^2]/3
y=0
代x=3.5入iii
y=[(3.5+1)^2]/3
y=6.75
(x,y)=(-1,0) 和 (x,y)=(3.5,6.75)

(5)
2y=-x^2+2x+13 i
5x+y=0 ii
由i, y=(-x+2x+13)/2 iii
代iii入ii
5x+(-x^2+2x+13)/2=0
10x-x^2+2x+13=0
-x^2+12x+13=0
x=-1 和 x=13
代x=-1入ii
-5+y=0
y=5
代x=13入ii
5*13+y=0
y=-65
(x,y)=(-1,5) 和 (x,y)=(13,-65)

(6)
x^2+y^2+4x-12=0 i
x-y+6=0 ii
由ii,x+6=y iii
代iii入i
x^2+(x+6)^2+4x-12=0
2x^2+16x+24=0
x=-2 和 x=-6
代x=-2入iii
-2+6=y
y=4
代x=-6入iii
y=0
(x,y)=(-2,4) 和 (x,y)=(-6,0)

(7)
x^2+y^2+6x-8y=0 i
x+3y-14=0 ii
由ii, x=-3y+14 iii
代iii入i
(-3y+14)^2+6(-3+14)-8y=0
196-84y+9y^2+y^2-18y+84-8y=0
10y^2-110y+280=0
y=7 和 y=4
代y=7入iii
x=-3(7)+14
x=-7
代y=4入iii
x=-3(4)+14
x=2
(x,y)=(-7,7) 和 (x,y)=(2,4)

(1)

2x^2 + 3x + 6 = 5y --- (1)
2x - 10y + 11 = 0 --- (2)

From (2) :

x = (10y-11)/2 --- (3)

Sub (3) into (1) :

2[(10y-11)/2]^2 + 3(10y-11)/2 + 6 = 5y
50y^2 - 100y + 50 = 0
50(y^2-2y+1) = 0
50(y-1)^2 = 0
y = 1 --- (4)

Sub (4) into (3) :

x = [10(1)-11]/2
= -1/2

Answer : x = -1/2, y = 1.

(2)

2x^2 - 3x - y = 10 --- (1)
5x + 3y = 2 --- (2)

From (2) :

y = (2-5x)/3 --- (3)

Sub (3) into (1) :

2x^2 - 3x - (2-5x)/3 = 0
3x^2 - 2x - 1 = 0
(3x+1)(x-1) = 0
x = -1/3 or 1

When x = -1/3,

y = [2-5(-1/3)]/3
= 11/9

When x = 1,

y = [2-5(1)]/3
= -1

Answer : x = -1/3, y = 11/9; x = 1, y = -1.

(3)

x^2 - 4x - 2y = 9 --- (1)
2x - y = 3 --- (2)

From (2) :

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

Sub (3) into (1):

x^2 - 4x - 2(2x-3) = 9
x^2 - 8x - 3 = 0
x = 4 ± √19

When x = 4 + √19,

y = 2(4+√19) - 3
= 5 + 2√19

When x = 4 - √19,

y = 2(4-√19) - 3
= 5 - 2√19

Answer : x = 4+√19, y = 5+2√19; x = 4-√19, y = 5-2√19.

(4)

x^2 + 2x + 1 = 3y --- (1)
3x - 2y + 3 = 0 --- (2)

From (2):

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

Sub (3) into (1) :

x^2 + 2x + 1 = (3x+3)/2
2x^2 + x - 1 = 0
(2x-1)(x+1) = 0
x = -1 or 1/2

When x = -1,

y = [3(-1)-3]/2
= -3

When x = 1/2,

y = [3(1/2)-3]/2
= 3/4

Answer : x = -1, y = -3; x = 1/2, y = 3/4.

(5)

2y = -x^2 + 2x + 13 --- (1)
5x + y = 0 --- (2)

From (2) :

y = -5x --- (3)

Sub (3) into (1) :

2(-5x) = -x^2 + 2x + 13
x^2 - 12x - 13 = 0
(x-13)(x+1) = 0
x = -1 or 13

When x = -1

y = -5(-1)
= 5

When x = 13

y = -5(13)
= -65

Answer : x = -1, y = 5; x = 13, y = -65.

(6)

x^2 + y^2 + 4x - 12 = 0 --- (1)
x - y + 6 = 0 --- (2)

From (2) :

y = x + 6 --- (3)

Sub (3) into (1)

x^2 + (x+6)^2 + 4x - 12 = 0
2x^2 + 16x + 24 = 0
2(x+2)(x+6) = 0
x = -6 or -2

When x = -6,

y = -6 + 6
= 0

When x = -2,

y = -2 + 6
= 4

Answer : x = -6, y = 0; x = -2, y = 4.

(7)


x^2 + y^2 + 6x - 8y = 0 --- (1)
x + 3y - 14 = 0 --- (2)

From (2) :

x = 14 - 3y --- (3)

Sub (13) into (1) :

(14-3y)^2 + y^2 + 6(14-3y) - 8y = 0
10y^2 - 110y + 280 = 0
10(y-7)(y-4) = 0
y = 4 or 7

When y = 4,

x = 14 - 3(4)
= 2

When y = 7,

x = 14 - 3(7)
= -7

Answer : x = 2, y = 4; x = -7, y = 7.