Question

1. 2x-y=4

x=5+y

2. 2x+y=3

x=4+2y

3. 4x-3y=2

y=4+2x

Answer 1

1)
{2x-y=4     
{x=5+y

{2(5+y)-y=4
{x=5+y

{10+2y-y=4
{x=5+y

{y+10=4  /-10
{x=5+y

{y= -6
{x=5+y

{y= -6
{x=5+(-6)

{y= -6
{x=5-6

{y= -6
{x= -1

SPRAWDZENIE:
* 2x-y=4
2*(-1)-(-6)=4
-2+6=4
4=4
* x=5+y
-1=5+(-6)
-1=5-6
-1= -1

2)
{2x+y=3     
{x=4+2y

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

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

{5y+8=3    /-8
{x=4+2y

{5y= -5    /:5
{x=4+2y

{y= -1
{x=4+2y

{y= -1
{x=4+2*(-1)

{y= -1
{x=4-2

{y= -1
{x=2

SPRAWDZENIE:
* 2x+y=3
2*2+(-1)=3
4-1=3
3=3
* x=4+2y
2=4+2*(-1)
2=4-2
2=2

3)
{4x-3y=2     
{y=4+2x

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

{4x-12-6x=2
{y=4+2x

{-2x-12=2    /+12
{y=4+2x

{-2x=14    /:(-2)
{y=4+2x

{x= -7
{y=4+2x

{x= -7
{y=4+2*(-7)

{x= -7
{y=4-14

{x= -7
{y= -10

SPRAWDZENIE:
* 4x-3y=2
4*(-7)-3*(-10)=2
-28+30=2
2=2
* y=4+2x
-10=4+2*(-7)
-10=4-14
-10= -10