how do i solve the system of equations exactly?

a)
y= 2x+1 (1)
y= x-1 (2)
substitute y in (1) as "x-1"

x-1=2x+1, transpose!
into
-1-1 = 2x-x
-2=x
use (2) to know y
y= -2-1=-3
answers;
x=-2
y=-3

b).
20x - y = 50 (1)
5x +y = 250 (2)

substitute y in (1) as 250-5x
you get 20x = 50 + 250 - 5x because you will transpose "-y" in (1) to the other side and it will become positive.

then,

20x=300-5x
20x+5x=300
25x=300
x=12

5x + y = 250
5(12)+ y = 250
60 + y = 250
y= 250-60
y= 190

answers:
x= 12
y= 190

Qa:
Value of x:
2x + 1 = x - 1
x = - 2

Value of y (1st equation):
= - 2 - 1
= - 3

Answer: x = - 2, y = - 3

Proof (2nd equation):
- 3 = - 2 - 1
- 3 = - 3

Qb:
y in terms of x:
20x - y = 50
y = 20x - 50

5x + y = 250
y = 250 - 5x

Value of x:
20x - 50 = 250 - 5x
25x = 300
x = 12

Value of y (1st equation):
= 20(12) - 50
= 240 - 50
= 190

Answer: x = 12, y = 190

Proof (2nd equation):
5(12) + 190 = 250
60 + 190 = 250
250 = 250

a)
y = 2x + 1 (solve by using elimination)
y = x - 1

....y = 2x + 1
‒) y = ..x .- 1
-------------------------
....0 = ..x + 2

0 = x + 2
x = -2

y = x - 1
y = -2 - 1
y = -3

∴ x = -2, y = -3

= = = = = = = = = = = = = = = =

b)
20x - y = 50 (solve by using substitution)
5x + y = 250

20x - y = 50
y = 20x - 50

5x + y = 250
5x + (20x - 50) = 250
5x + 20x - 50 = 250
25x = 250 + 50
x = 300/25
x = 12

20x - y = 50
20(12) - y = 50
240 - y = 50
y = 240 - 50
y = 190

∴ x = 12, y = 190

a)
y=2x+1
y=x-1
Therefore, 2x+1 = x-1
x = 2
plug this x into equation (1)
y = 2(2) +1 = 5

b)
Add the two equations:
25x = 300
x = 12
plug this x into equation (1)
20 (12) - y = 50
240 - y = 50
-y = -190
y = 190

There are several methods for solving system of equations, and the two most common ways are called substitution and elimination. I will solve a using the former and b using the latter.

a) We are given two expressions that are both = to y; therefore, we can set them equal to each other:
2x+1=x-1
x=-2 =>y=-3

b) Elimination is a bit more tricky. Notice that the equations have -y and y respectively, so if we add these, they will cancel out a variable:
25x=300
x=12=>y=190

Well in b, you set it up like an addition problem, and see there is a -y on top and a +y on the bottom, so they cancel. That leaves you with 25x=300 (since we are adding everything else too). Then just divide both sides by 25 and you get x=12

a)
y=2x+1
-y=-x+1
________
x+2=0
x = -2
y = -3

b)
20x-y = 50
20x+4y=1000
-5y = -950
y = 190
x = 12