2. 2 1/10 2/10 3/10 (1)4/10 (2) 5/10 6/10 A=B=C 8/10 7/10 (1) 9/10 (2) 10/10

1. 2 .2. 2 .

18 2 x 1 y . x,y ? 2 x 2x1 y y 2x+y= 18

2 2 : 2 ) 2x + y = 18 ax + by + c = 0 (a,b,c:,a0,b0)2x + y 18 = 0 x +3y = 0

2 2 () : x,y ) x,y: , 5x + y = 13 ?) x=1 , x=2 , x=1, y=8 x=2, y=3 : 51+y =13 y=52+y =13 y= (1,8) (2,3) 83x=3 ,53+y =13 y=2

x,y: , 2x + y = 10 ?123) x=1,2,3, , y ? 456 x=1 , 21+y =10 y= 8 x=2 , 22+y =10 y= x=3 , 23+y =10 y= 64202) (1,8) (2,6) (3,4) (4,2)864

x,y: , 3x + 2y = 20 ? x=1 , 31+2y =20 y = x=2 , 32+2y =20 y = x=3 , 33+2y =20 y = x=4 , 34+2y =20 y =74) (2,7) (4,4) (6,1) 741)

x,y x + ay 4 = 0 (2,2) , a ? x = 2, y = 2 2 + a2 4 = 0 ) a = 3 ) 2a = 2+4

(2,1),(3,a) x,y 3x by = 1 a ? x = 2, y = 1 32 b1 = 1 b = 5 ) b = 5 : 3x 5y = 1 3(3) 5a = 1 5a = 10 ) a = 2

? 1) x,y : x + y = 7 2) x,y : x + 3y = 10 (1,6)(2,5)(3,4)(4,3)(5,2)(6,1) (1,3) (4,2) (7,1)

2 .

x,y : x + 3y = 10 ? x=1 , 1 + 3y = 10 y = x=2 , 2 + 3y = 10 y = x=3 , 3 + 3y = 10 y = x=4 , 4 + 3y = 10 y =3) (1,3) (4,2) (7,1) 321)2

: 2 ) x,y : x + 3y = 10 (1,3) (4,2) (7,1) 1. 2.

1) x + y = 6 2) x + 4y = 10 (1,5) (2,4) (3,3) (4,2) (5,1) (2,2) (6,1) x,y , ?

x,y : , x + 3y = 10 ?321 1. : . x + 3y = 10 2.

1) 2) (1,3) (3,2) (5,1) x + 2y = 7 ?3)

1) x + y = 4 2) 2x y = 3 (1,3) (2,2) (3,1) (1,1) (2,1) (3,3) x,y , ?

(1, 2) (2, a) 3x + by = 1 , a+b ? (1,2) x = 1, y = 2 31+b(2) = 1 b = 1 ) 2b = 13 : 3x + y = 1 x = 2, y = a 2b = 2 3(2) + a = 1 a = 7 ) 8

? 1) x,y : 2x + y = 7 2) x,y : 3x 2y = 5 (1,5)(2,3)(3,1) (1,1)(3,2)

1. 2 .2. .

100 x, 200 y 800 5 . x,y , x,y ? x + y = 5 x, y 100x + 200y = 800 x, y x = 2, y = 3

2 2 : 2 : x , y x= 2 , y= 3 :

123) 4565432) x=4, y=3 x, y 7 , 20. x y ? x + y = 7 2x + 4y = 20 x + y = 7 2x + 4y = 20 24436281(x, y:)

x,y: , ?) x=4, y=1 x + y = 5 2x + 3y = 11 1234432131

A={ (x,y)| x y = 2 } B ={(x,y)|2x+y = 10 } AB ?) x=4, y=2 x y = 2 2x + y = 10 3456712345182634425

x,y , ? : (4,2) x y = 2 2x + y = 10 ) x=4, y=2

???? x=3, y=b , ab ? 2x + y = 8 x y = a ) 23 +b = 8 b = 2 3 2 = a a = 1 ) 1

1. .2. .

A=B, C=D ? A = BC = DA + C B + D + A = BC = DA C B D = =

? + = 2x y = 5 4x + y = 13 6x 18 x = 3 ,

: ( )+ 2x y = 4 2x 3y = 12 4y = 8 y = 2 x = 3 2x 2 = 4 2x = 6

? 5x 2y = 2 2x 2y = 4 3x = 6 x = 2 y = 4 2 (2) 2y = 4 2y = 8 ++

x y = 5 2x + y = 1 ?(1)2x 3y = 7 2x y = 3 (2)+ 3x = 6 x = 2 ) x =2 , y =3 2 y = 5 y = 3 2y = 4 y = 2 2x (2) = 3

?3x y = 2 3x + y = 10 ) x = 2 , y = 42y = 8 y = 4 3x 4 = 2 3x = 6 x = 2 ????

.

, ? + = 17 x 3y = 15 2x + y = 2 3x 2y , . = 13 x 3y = 15 2x + y = 2 x 4y

?3 x 3y = 15 2x + y = 2 7x = 21 x = 3 3 3y = 15 3y = 12 + y = 4

2x y = 4 5x +3y = 1 ?(1)3x 4y = 15 2x 3y = 7 (2)+ 11x = 11 ) x = 1 , y = 2 y = 51 3x 4(51) = 15 3 6x 3y = 12 5x + 3y = 1 x = 1 21 y = 4 y = 2 236x 8y = 30 6x 9y = 21 + 3x = 219 + x = 73) x = 51 , y = 73

A={ (x,y) | 4x + 3y = 5 } B={ (x,y) | x y = 3 } AB ? 4x + 3y = 5 x y = 3 + 7 x = 14 ) x = 2 , y = 1 3 4x + 3y = 5 3x 3y = 9 x = 2 2 y = 3 y = 1 y = 1

x=1, y=2 , a+b ?)ax + by = 0 bx + ay = 3 x = 1, y = 2 a + 2b = 0 b + 2a = 3 a = 2 3b = 3 2a + 4b = 0 b + 2a = 3 b = 13) 1

? 2x y = 2 4x + 3y = 4 6x 3y = 6 4x + 3y = 4 3+10x = 10 x = 1 2 y = 2 y = 0 ) x = 1 , y = 0????

1. .

y 2x 5 ? y = 2x 5 3x 4y = 5 3x 4 (2x 5) = 5

: ( ) x = 3 5x = 15 y = 2x 5 3x 4y = 5 3x 4 (2x 5) = 5 3x8x+20 = 5 y = 23 5 = 1

? y = 1 5y = 5 x = 3y + 2 2x + y = 1 2(3y + 2) + y = 1 6y+4+ y = 1 x = 31+ 2 = 1) x = 1 , y = 1

x = y +1 2x + y = 1 ?(1) y = 4x 1 y = 2x 2 (2)) x = 0 , y = 1 2(y+1)+y = 1 2y+2+y = 1 y = 1 y = 1 x = 1+1= 0 4x 1 = 2x 2 2x = 1

? 4x = 5 2x + 3y = 2 2x + y = 1 2x +3(2x1) = 2 2x6x3 = 2 y = 2x 1 2x + 3y = 2

?3x y = 1 2x 3y = 4 y = 3x 1(y ) y = 3x +1 7x = 7 2x 3(3x+1) = 4 2x9x3 = 4 x = 1 y = 3(1) + 1 = 2 ) x = 1 , y = 2

x y 1:3 a ?)3x ay = 6 2x + y = 5 x : y = 1 : 3 y = 3x2x + y = 52x + 3x = 55x = 5x = 1y = 33 3a = 6 3a = 3a = 1

? y = 2x 2 4x + 3y = 4 (1)) x = 1 , y = 0 4x + 3(2x 2) = 4 4x + 6x 6 = 4 10x = 10 x = 1 y = 21 2 = 0 2x = y 1 2x = 3y + 3(2) y 1 = 3y + 3 2y = 4 y = 22x = 2 1

1. . 2. .

: . 3x 2(x+3y ) = 9 3(x y) = 3 9y + 4x = 12 ) x = 3 , y = 1 x 6y = 9 3x + 6y = 3 x = 3 3 6y = 9 y = 1 3x 2x 6y = 9 3x 3y = 3 9y

? 3(2x 1) 3y = 6 8x (2x 3y) = 3 6x 3 3y = 6 8x 2x +3y = 3+ 12x = 12 6x 3y = 9 6x + 3y = 3 x = 1) x = 1 , y = 1 6 3y = 9 y = 1

? 0.2x 0.4y = 0.05 10020x 40y = 5 12 9x + 8y = 12

: . : 10 : 0.2x 0.3y = 1 102x 3y = 10 6 x +3y = 2 + 3x = 12 x = 4 24 3y = 10 3y = 2

?0.1x+0.2y = 0.3 0.3x0.2y = 0.5 (1)(2) x+2y = 3 3x2y = 5 + 4x = 8 x = 2 2x+3y = 6 3x+4y = 8 6x+9y = 18 6x+8y = 16) x = 0 , y =2 y = 2

?????0.3x0.1y = 1 3x y = 10 3x + 4y = 5 5y = 5 y = 1 3x (1) = 10 3x = 9 x = 3 ) x = 3 , y = 1

1. A=B=C . 2. , .

? A = B B = C A, B, C A=B=C . A = B A = C A = C B = C

: A=B=C .

A=B=C A = B B = C A = B A = C A = C B = C 2x y = 2 3x 2y = 22 4x 2y = 4 3x 2y = 2 x = 2 y = 2) 2x y = 3x 2y = 2

?1) 2x5y+4 = 7x+3y = 4x y 2) 3x+2y = 2x+y+9 = 4 2x5y+4 = 4x y 7x+3y = 4x y 2x 4y = 4 3x +4y = 0+ x = 4) x = 4 , y = 3 3x +2y = 4 2x+y+9 = 42 3x +2y = 4 4x +2y = 10 7x = 14) x = 2, y = 1

1) . 2) . x + 2y = 2 x + y = 3 x + 2y = 2 2 x + 2y = 6 0 = 4

, ab ? x + 2y = 3 ax by = 9 . , .3 a = 3, b = 6 ) a b = 9

???? , a ? ax + 2y = 6 4x + y = 1 . .2) a = 8

1. . 2. .

100 50 17 . 1250 . 100 ? x + y = 17 100x + 50y = 1250 x = 8, y = 9 100: 50 : x y ) 100 : 8

1) x, y ( x, y ) 2) ( 2 ) 3) ( ) 4) ( )

2 1 2100, 1 2 1800 . ? : x, : y 2x + y = 2100 x + 2y = 1800 3x = 2400 x = 800 2800 + y = 2100 y = 500 2800+500 = 800+2500 = 2100 1800) : 800, : 500

1 500 1 1000 8 5000 . ? : x, : y x + y = 8 500x + 1000y = 5000 : 8 x = 6, y = 2 ) : 6, : 2 : 5006+10002

35. 20 2 1 . ? : x, : y x y = 3520 x + 20 = 2(y+20) 1 x = 51, y = 16 ) : 51, : 16

. 14, 36 . ? ) : x, : y x + y = 14 10x+y = 10y+x 3659 = 95 36 ) 59 x = 5, y = 9

, 3 2 1 3 7000 . 1 1 ? 1 : x, 1 : y3,2 3x + 2y = 70001,3 x + 3y = 7000 x = 1000, y = 2000 ) 1 : 1000 1: 2000

1. . 2. .

?1. 4 km 3 4 32. 8 km 4 km , () = () ()

x km () y km ( ) x + y = 32 x = 27, y = 5 ) 27km 32 36 4 2 . ?

: xkm, : ykm x + y = 6 x = 2, y = 4 6km. 3km 6km 1 20 . ?) : 2km

?1. 5% x g ?2. 200 g x g , ? ( ) = () ( )

3% 6% 5% 240g . g ? x + y = 240 x = 80, y = 160 ) 3%: 80g 6%: 160g x g y g 240 g

x g (8%) 160 g (5%) y g (4%)+ x + y = 160 x = 40, y = 120 ) 8%: 40g 4%: 120g8% 4% 5% 160g . g ?

1200. 10% 20% 2% . ? : x, : y x + y = 1200 x = 720, y = 480

A,B A 20%, 30% , B 40%, 10% . 30g, 20g A,B g ? 30 gA : x g B : y g 20 g ) A: 50g B: 50g

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