Question

1. Rozwiąż układy równań metodą powstawania.
a) x+3y=3
x-y=5
b) 2x-y=10
x+5y=-17
c) 3m+n=9
2m-5n=-11
d) 6x-3y=9
x+5y=-9,5

Answer 1

A) x+3y=3
x-y=5

x = 3 - 3y
3 - 3y - y = 5

-4y = 5 - 3
-4y = -2 |:(-4)
y = ½

x = 3 - 3*½
x = 3 - 1½
x = 1½

b) 2x-y=10
x+5y=-17

-y = 10 - 2x
y = -10 +2x

x + 5(-10 + 2x) = -17
x - 50 + 10x = -17
9x = -17 + 50
9x = 33 |:9
x = 3⅔

y = -10 + 2*3⅔
y = -10 + 2*11/3 = -10 + 22/3
y = -30/3 + 22/3 = -8/3
y = -2⅔

c) 3m+n=9
2m-5n=-11

n = 9 - 3m
2m - 5(9 - 3m) = -11
2m - 45 + 15m = -11
17m = -11 + 45
17m = 34 |:17
m = 2

n = 9 - 3m
n = 9 - 3*2
n = 9 - 6
n = 3

d) 6x-3y=9
x+5y=-9,5

x = -9,5 - 5y

6(-9,5 - 5y) - 3y = 9
-57 - 30y - 3y = 9
-33y = 9 + 57
-33y = 66 |:(-33)
y = -2

x = 9,5 - 5y
x = -9,5 - 5*(-2)
x = -9,5 + 10
x = -0,5

Answer 2

A) x +3y = 3
x - y = 5 /*3
x+3y = 3
3x - 3y = 15
4x= 45/:4
x = 11,25
b) 2x - y = 10 /*5
x+5y =-17
10x - 5y= 50
x+5y = -17
11x =33 /:11
x= 3

c) 3m +n =9 /*5
2m- 5n =-11
15m +5n =45
2m - 5n = -11
17m = 34/:17
m=2

d) 6x - 3y = 9 /*5
x + 5y = -9,5 / *3
30x - 15y = 45
3x + 15y = -28,5
33x = 16,5 /:33
x = 0,5

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