How to solve by subsitutions? Step by step guide?

Question

1) y=-3x-10   -4x-3y=15     2) 6x-4y=2    y=6x-14

 

* Please show work so I can learn from this and understand. Thank you! *

Answer 1

1) y=-3x-10   

-4x-3y=15

Substitute y = -3x - 10 in -4x-3y=15

-4x - 3(-3x-10 ) = 15

Apply distributive property: a(b + c) = ab + ac. Distribute - 3.

-4x + 9x + 30 = 15

5x + 30 = 15

Subtract 30 from each side

5x = -15

Divide each side by 5

x = -3

 

Substitute x = -3 in y = -3x - 10

y = -3(-3) - 10

y = 9 - 10 = -1

(x, y) = (-3, -1)

Answer 2

2) 6x-4y=2

  y=6x-14

Substitute y = 6x - 14 in 6x - 4y = 2

6x - 4(6x - 14) = 2

Distribute 4

6x - 24x + 56 = 2

-18x + 56 = 2

Subtract 56 from each side

-18x = -54

Divide each side by -18

x = 3

Substitute x = 3 in y = 6x - 14

y = 6 * 3 - 14

y = 18 - 14

y = 4

solution to the system is (3, 4)