solving system of equations?

1)
x + 4y = 19 (solve by using subtitution)
5x + y = 0

x + 4y = 19
x = 19 - 4y
5x = 5(19 - 4y)

5x + y = 0
5(19 - 4y) + y = 0
95 - 20y + y = 0
-20y + y = -95
-19y = -95
y = -95/-19
y = 5

x + 4y = 19
x + 4(5) = 19
x + 20 = 19
x = 19 - 20
x = -1

∴ x = -1 , y = 5

= = = = = = = =

2)
a - b = 25 (solve by using addition)
3a + 4b = 4

a - b = 25
4(a - b) = 4(25)
4a - 4b = 100

...4a - 4b = 100
+ 3a + 4b = 4 (addition)
----------------------
7a = 104

7a = 104
a = 104/7

a - b = 25
104/7 - b = 25
b = 104/7 - 25
b = 104/7 - 175/7
b = -71/7

∴ a = 104/7 , b = -71/7

- 5x - 20y = - 95
5x + y = 0---------------------ADD

- 19y = - 95
y = 5

5x + 5 = 0
x = - 1

x = - 1 , y = 5

x + 4y = 19
5x + y = 0 or y = -5x
now substitute this value in equation 1 as
x + 4(-5x) = 19
x - 20x = 19
-19x = 19
so x = -1
hence y = -5(-1) = 5


a - b = 25
3a + 4b = 4
multiply equation 1 by 4 and add to the equation 2
4a - 4b = 100
3a + 4b = 4
by adding them we get 7a = 104
so a = 104/7
substitute this value in equation 1
b = a - 25
=104/7 - 25
= - 71/7
hence a = 104/7 and b = -71/7

one way to do it is. you could take one equation and solve for a single variable. for example.
x + 4y = 19 becomes x=19 - 4y
then you would substitute this equation (x =19 - 4y) into the other one (5x + y = 0) and solve for y. take the and plug it into the first equation (x=19 - 4y) and get x. for this problem I got x= -1 and y=5.

for the 2nd problem i got b = -71/7 and a=104/7