SOLUTION: Solve the following pairs of simultaneous equations: X+2y=3,X-2y=3 Y=2×-1,Y=3x-2 2y=6x-4,Y=3x-2

1. 

x + 2y = 3,
x - 2y = 3.

Add the two equations (both sides). The terms with "y" will cancel, and you will get

2x = 6, which implies x = 3.

Now, substitute the found value x= 3 into the first equation. You will get

3 + 2y = 3  --->  2y = 0  --->  y= 0.

Answer. The solution is x= 3, y= 0.
        The method I applied is called the Elimination method.




2. 

y = 2x - 1,
y = 3x - 2.

Since the left sides are identical, the right sides are equal:

2x - 1 = 3x - 2  --->  -1 + 2 = 3x - 2x  --->  1 = x  --->  x = 1.

Now, substitute the found value x= 1 into the first equation. You will get

y = 2*1 - 1 = 2 - 1 = 1.

Answer.  The solution is x= 1, y= 1.




3.

2y = 6x - 4, 
 y = 3x - 2.

In the first equation, divide both sides by 2. You will get an equivalent equation

 y = 3x - 4.

Compare it with the second equation.
You see that they are identical.

So, your system is actually one equation for two unknowns, since the second equation is equivalent to the first one.

Geometrically, these two equations represent one straight line.

The original system has infinitely many solutions.