Solve each system by substitution? Please show all steps

Question

1)
y = 5x - 10
y = 3x + 8

2)
3x + y = 2
4x + y = 20

Answer 1

1)  Given equations are

y=5x-10...........(1)

y=3x+8............(2)

Substitute y=3x+8 in equation (1)

3x+8=5x-10

Add 10 to each side

3x+8+10=5x-10+10

3x+18=5x

Subtract 3x from each side

3x-3x+18=5x-3x

18=2x

Divide each side by 2

18/2=2x/2

x=9

Answer 2

1)  Given equations are

y=5x-10...........(1)

y=3x+8............(2)

Substitute y=3x+8 in equation (1)

3x+8=5x-10

Add 10 to each side

3x+8+10=5x-10+10

3x+18=5x

Subtract 3x from each side

3x-3x+18=5x-3x

18=2x

Divide each side by 2

18/2=2x/2

x=9

Substitute x=9 in equation (1)

y=5(9)-10

y=45-10

y=35

Comments

The solution of the system :  y = 5x - 10

                                         y = 3x + 8   is x = 9 and y = 35.

Answer 3

2)  Given equations are

3x+y=2...........(1)

4x+y=20............(2)

Solve equation (1) for y

y=2-3x

Substitute y=2-3x in equation (2)

4x+2-3x=20

x+2=20

Subtract 2 from each side
x+2-2=20-2

x=18

Substitute x=18 in equation (2)

4(18)+y=20

72+y=20

Subtract 72 from each side

72-72+y=20-72

y=-52

Solution (x,y) = (18,-52).