Solving an equation.?

Question

3x-6y=12
2x-4y=7

2x+y=6
3x-y=-1

Answer 1

3x + 6y = 12 .....(1)
2x - 4y = 7 ........(2)

Fr. (1) : (1)/3
x + 2y = 4
x = 4 - 2y ......(3)

Subs (3) into 2
2(4 - 2y) - 4y = 7
8 - 4y - 4y= 7
8y = 1
y = 1/8

Subs y = 1/8into (3)
x = 4 - 2(1/8)
x = 3 3/4
Ans x= 3 3/4, y = 1/8


2x + y = 6 .......(1)
3x - y = -1 ......(2)

(1) + (2):
5x = 5
x = 1

Subs x = 1 into (1)
2(1) + y = 6
y = 4
Ans x= 1, y = 4

Answer 2

3x-6y =12
2x-4y =7 can be rewritten as 2x=7+4y or x= 2y+3.5
so 3(2y+3.5) -6y =12 this leads to an impossibility since you have 10.5=12. Explanation if you multiply the second equation by 3/2) , the left side is equal to the right side of the first


2x+y = 6 (1)
3x-y = 1 (2) add (1) and (2)
5x=7
x = 7/5 put this value in (1)
14/5 +y =6
y = 6-14/5 = 16/5

proof 2(7/5) +16/5 = (14+16)/5 =6

so x=7/5 y=16/5

Answer 3

For the first set, multiply the first equation by 2 and the second by -3--then add them together to get: you run into trouble because it turns out that these two lines are parallel and, therefore, have no intersection.
For the second set of equations, simply add them together to get 5x=5, which solves to give you x=1. Substitute this back into the first to get 2+y=6--or y=4.