Question

Rozwiąż układy równań metodą podstawiania

a) 2x - 2y = 7
4x + 3y = 21



c) 2x + 3y =14
3x - 2y = 8


d) 1/2 x - 2y = 8
2x + 5y = 6

Answer 1

A) 2x - 2y = 7
4x + 3y = 21

2x=7+2y /2
4x+3y=21

x=3,5 +y
4(3,5+y)+3y=21

x=3,5+y
14+4y+3y=21

x=3,5+y
7y=7

x=3,5+y
y=1

x=3,5+1
y=1

x=4,5
y=1

c)2x + 3y =14
3x - 2y = 8

2x=14-3y /2
3x-2y=8

x=7-1,5y
3(7-1,5y)-2y=8

x=7-1,5y
21-4,5y-2y=8

x=7-1,5y
-6,5y=-13 /(-6,5)

x=7-1,5y
y=2

x=7- 1,5(2)
y=2

x=4
y=2

d)1/2 x - 2y = 8
2x + 5y = 6

0,5x=8+2y /0,5
2x+5y=6

x=16+4y
2(16+4y)+5y=6

x=16+4y
32+8y+5y=6

x=16+4y
13y=-26 /13

x=16+4y
y=-2

x=16+4(-2)
y=-2

x=8
y=-2

Answer 2

A)
2x - 2y = 7
4x + 3y = 21

2x = 7 + 2y
4x + 3y = 21

2x = 7 + 2y
14 + 4y + 3y = 21

2x = 7 + 2y
7y = 7 / ÷ 7

2x = 7 + 2y
y = 1

2x= 7 +2
y = 1

2x = 9
y = 1

x = 4,5
y = 1


C)
2x + 3y = 14
3x - 2y = 8

2x = 14 - 3y
14 - 3y + 7 - 1,5y - 2y = 8

2x = 14 - 3y
-6,5y = -13 /÷ (-6,5)

2x = 14 - 3y
y = 2

2x = 14 - 6
y = 2

2x = 8 / ÷ 2
y = 2

x = 4
y = 2

D)
½x - 2y = 8
2x + 5y = 6

½x = 8 + 2y
32 + 8y + 5y = 6

½x = 8 + 2y
13y = -26 / ÷ 13

½x = 8 + 2y
y = -2

½x = 8 - 4
y = -2

½x = 4 / ÷ ½
y = -2

x = 8
y = -2