Question

Rozwiąż układy równań metodą podstawiania:

a) 3x-4y= -1
2x+y= 3

b)2x+3y= -4
5x+6y= -7

c)7x+9y= 8
9x-8y= 69

d)x/2-y/3= 1
x/4+2y/3= 8

e)x+y/2+2y= 0

Answer 1

A)
3x-4y= -1
2x+y= 3

y = 3 - 2x
3x - 4*(3 - 2x) = -1

y = 3 - 2x
3x - 12 + 8x = -1

y = 3 - 2x
11x = 11/:11

y = 3 - 2x
x = 1

y = 3 - 2*1
x = 1

y = 1
x= 1

b)
2x+3y= -4
5x+6y= -7

2x = -4 - 3y /:2
5x+6y= -7

x = - 2 - 3/2y
5*(- 2 - 3/2y) + 6y= -7

x = - 2 - 3/2y
- 10 - 15/2y + 6y = -7

x = - 2 - 3/2y
- 3/2y = 3 /: - 3/2

x = - 2 - 3/2y
y = -2

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

x= -2 + 3
y = -2

x = 1
y = -2

c)
7x+9y= 8
9x-8y= 69

7x = 8 - 9y /:7
9x-8y= 69

x= 8/7 - 9/7y
9* (8/7 - 9/7y) -8y= 69

x= 8/7 - 9/7y
72/7 - 81/7y - 8y = 69

x= 8/7 - 9/7y
- 81/7y - 56/7y = 483/7 - 72/7

x= 8/7 - 9/7y
- 137/7y = 411/7 / * - 7/137

x= 8/7 - 9/7y
y = -3

x= 8/7 -9/7* - 3
y = -3

x = 8/7 + 27/7
y = -3

x = 5
y = -3


d)
x/2-y/3= 1/*6
x/4+2y/3= 8 / *12

3x - 2y = 6
3x + 8y = 96

3x = 6 + 2y /: 3
3x + 8y = 96

x = 2 + 2/3y
3*(2 + 2/3y) + 8y = 96

x = 2 + 2/3y
6 + 2y + 8y = 96

x = 2 + 3/2y
10y = 90

x = 2 + 2/3y
y = 9

x = 2 + 2/3*9
y = 9

x = 2 + 6
y = 9

x = 8
y = 9


e)
x+y/2+2y= 0 / *2
2x + y + 4y = 0
2x = -5y
x = -5/2y