Question

Rozwiąż układy równań dowolną metodą:
a) { x + y = 6 x - y = 2
b) { x + y = 6 2x - y = 12
c) 3 x + 2y = 4
1,5x + 6y = 12
d) { 3x + 2y = 2 x - y = 4
e) { 2x - y = 16 x + 3y = 17

Z góry dzięki:)

Answer 1

A) x + y = 6
x - y = 2

x=6-y
6-y-y=2

x=6-y
6-2y=2

x=6-y
-2y=2-6

x=6-y
-2y=-4 |:(-2)

x=6-y
y=2

x=6-2
y=2

x=4
y=2

b) x + y = 6
2x - y = 12

x=6-y
2(6-y)=12

x=6-y
12-2y=12

x=6-y
-2y=12-12

x=6-y
-2y=0 |:(-2)

x=6-y
y=0

x=6-0
y=0

x=6
y=0

c) 3 x + 2y = 4
1,5x + 6y = 12 |:1,5

3x+2y=4
x=8-4y

3(8-4y)+2y=4
x=8-4y

24-12y+2y=4
x=8-4y

-10y=-20 |:(-10)
x=8-4y

y=2
x=8-4*2

y=2
x=8-8

y=2
x=0

d) 3x + 2y = 2
x - y = 4

3x+2y=2
x=4+y

3(4+y)+2y=2
x=4+y

12+3y+2y=2
x=4+y

5y=-10 |":5
x=4+y

y=-2
x=4-2

y=-2
x=2

e) 2x - y = 16
x + 3y = 17

-y=-2x+16 |*(-1)
x+3y=17

y=2x+16
x+3(2x+16)=17

y=2x+16
x+6x+48=17

y=2x+16
7x=-31 |:7

y=2x+16
x= -³¹/₇

y=2*(-³¹/₇)+16
x=-4³/₇

y=(-⁶²/₇)+16
x=-4³/₇

y= -8⁶/₇ + 16
x=-4³/₇

y=7¹/₇
x=-4³/₇

Answer 2

A) x + y = 6
x = 2 + y
2 + 2y = 6
2y = 6 - 2
2y = 4
y = 2
x + 2 = 6
x = 6 - 2
x = 4
b)x + y = 6
2x - y = 12
x = 6 - y
2 * (6 - y) + y = 6
12 - 3y = 6
-3y = -6
y = 2
x + 2 = 6
y = 4
c) 3 x + 2y = 4
1,5x + 6y = 12
1.5x = 12 - 6y
x = 8 - 4y
3 * (8 - 4y) +2y = 4
24 + 2y = 4
2y = 4 - 24
2y = -20
y = -10
3x - 20 = 4
3x = 24
x = 8