solve the system of linear equations by substitution.

Question

y=x+3

y=5x-5

 

 

 

y=3x-1

y=x-7

 

 

 

x=5y+2

x-4y=5

Answer 1

y=x+3
y=5x-5

 

x+3=5x-5

4x=8

x=2

y=5

y=3x-1
y=x-7

 

x-7=3x-1

2x=-6

x=-3

y=-10

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

 

x=5+4y

 

5+4y=5y+2

y=3

 

x=5+(4)(3)

x=5+12

x=17

Answer 2

first one:

 

y=x+3  

move the 3 to the other side

y-3=x

 

substitute the x into the other equation

y=5(y-3)-5

distribute the 5

y=5y-15-5

collect terms

y=5y-20

move y's to one side

-4y=-20

divide by negative 4 on both sides

y=5

 

substitute back into first equation

y=5=x+3

5=x+3

subtract 3 from both sides

x=2

 

the first one is y=5 x=2

 

For the second and third, follow the same pattern.