Question

Układy równań pierwszego stopnia z dwiema niewiadomymi:
{10(y+2)+3(x-5)=x-5
{25(y+2)+3(x-5)=-10
Następny przykład
{2(2x-y)+3(x+3y)=42
{5(x+3y)-8(2x-y)=-32

Answer 1

A){10(y+2)+3(x-5)=x-5
{25(y+2)+3(x-5)=-10

10y+20+3x-15=x-5
25y+50+3(-5y-5)-15=-10

2x=-10y-20-5+15
25y+50+3(-5y-5)-15=-10

2x=-10y-10
25y+50+3(-5y-5)-15=-10

x=-5y-5
25y+50+3(-5y-5)-15=-10

x=-5y-5
25y+50-15y-15-15=-10

x=-5y-5
25y-15y=-10+15+15-50

x=-5y-5
10y=-30

x=-5y-5
y=3

x=-5(-3)-5
y=3

x=15-5
y=3

x=10
y=3

B){2(2x-y)+3(x+3y)=42
{5(x+3y)-8(2x-y)=-32

4x-2y+3x+9y=42
5x+15y-16x+8y=-32

7x+7y=42
-11x+23y=-32

7x=42-7y
-11x+23y=-32

x=6-y
-11(6-y)+23y=-32

x=6-y
-66+11y+23y=-32

x=6-y
34y=-32+66

x=6-y
34y=34

x=6-y
y=1

x=6-1
y=1

x=5
y=1