Solve by elimination: 3x-2y=3 and -6x+4y=-6

Question

Whenever I try to solve this I get 0=0. I don't know what that means or if that's correct. Please help.

Answer 1

 

Yes, you are correct.

 

When you multiply the first equation by -2 and add it to the second equation,

you do in fact get 0 = 0.

 

That means the two equations represent the same line.

There are infinitely many solutions.

 

Let's take the first equation.

3x - 2y = 3

 

Solving for y, 

 

 -2y = 3 - 3x

 

 2y = (3x - 3)

 

y = 3/2(x-1)

 

X is the free variable (independent variable).

 

Once selected, the value of y is calculated using that equation in bold above.

 

The solution set is { x ,   3/2(x-1) } for any real number x

 

 

 

Answer 2

The second equation is a multiple of the first (times -2).

The equations name the same line.

0 = 0 indicates this also.