I need help with algebra !

1
Select the ordered pair from the choices below that is a solution to the following system of equations:
2x = 8 - y
4x - 3y + 19 = 0

a. (-7, 22)
b. (10, -12)
c. (-2, 12)
d. (1/2, 7)
Question 2
Select the ordered pair from the choices below that is a solution to the following system of equations:
2y = 5x - 13
4x - 5y = 7

a. (-1/2,14/5)
b. (3, 1)
c. (-4, -1)
d. (-3, -2)
Question 3
Select the ordered pair from the choices below that is a solution to the following system of equations:
6x = 2 - y
2y + 3x = 4

a. (1/3, 0)
b. (0, 2)
c. (2/3, -6)
d. (-2, 14)

4
Which of the following systems of equations has no solution?

a. 7x - 5y = 10; 15y = 14x - 2
b. 3x - 5 = 3y; 6y - 1 = -6x
c. 5x - 3y = 9; 6y = 10x - 18
d. 2y = 5x - 10; 10x - 4y = 3
Question 5
Which of the following systems of equations has infinitely many solutions?

a. 5x + 5y = 11; 10y = 10x - 22
b. 8x - 3 = 6y; 12y - 6 = 4x
c. 5x - 7y = 4; 14y = 10x + 8
d. 5y = -x + 4; 3x + 15y = 12
Question 6
Classify the following system of equations:
-9x + 3y = 6
2y = 6x + 4

a. Consistent and independent
b. Inconsistent
c. Consistent and dependent

Question 1's answer is (D) because y=8-2x so 4x-3(8-2x)+19=0 -> 4x-24+6x+19=0 -> 10x-5=0 -> (x=1/2) -> y=8-2(1/2) -> y=8-1 -> (y=7)
Question 2's answer is (B) because y=(5x/2)-(13/2) so 4x-5((5x/2)-(13/2))=7 -> 4x-(25x/2)+(65/2)=7 -> 8x-25x+65=14 -> -17x=-51 -> (x=3) -> y=(5(3)/2)-(13/2) -> (y=1)
Question 3's answer is (B) because y=2-6x -> 2(2-6x)+3x=4 -> 4-12x+3x=4 -> 4-9x=4 -> -9x=0 -> (x=0) -> y=2-6(0) -> (y=2)
Thats all i got to before I realized that ive already got a headache and now im trying to help someone with math. But based on these answers, you get the basic idea. you just solve one equation for y, then plug that into the other equation wherever you see a y then solve it for x, then plug that x back into the original equation and solve for y as a contant. Hope this helps some, and sorry i cant give you all the answers.

1. d. (1/2, 7)
2.b. (3, 1)
3. b. (0, 2)