4x - y = 3 -------------- (1)
12x = y - 1 --------------(2)
Looking at the pair of simultaneous equations, we can use the substitution method since one of the variables has a coefficient that equals 1. From equation (1);
4x - 3 = y
[Note that when a positive value crosses to the other side of an equation, it becomes negative, and vice versa. Hence 3 crosses and becomes a negative, while y crosses and becomes a positive.]
If y = 4x - 3,
Then substitute for the value of y into equation (2)
12x = y - 1
12x = 4x - 3 -1
**Remember its no longer y, but its now 4x - 3**
12x = 4x - 3 - 1
12x = 4x -4
Subtract 4x from both sides of the equation (to eliminate it from the right hand side)
12x - 4x = 4x - 4x - 4
8x = - 4
Divide both sides of the equation by 8 (to eliminate it from the left hand side and have the x variable stand alone)
8x/8 = -4/8
x = - 1/2
Looking back at equation (1), when x = - 1/2, substitute for this value into equation (1)
4x - y = 3
4(- 1/2) - y = 3
- 2 - y = 3
Add 2 to both sides of the equation (to eliminate the - 2 on the left hand side and isolate the - y)
- 2 + 2 - y = 3 + 2
- y = 5
Multiply both sides of the equation by - 1 (to eliminate the negative sign in front of the y)
- y (-1) = 5 (-1)
y = - 5
Therefore, x = -1/2 and y = -5
As an ordered pair, your answer is
(-1/2, -5)