How do you solve this system of equations?

2x + 3y = 1

4x + 6y = 2

For some reason when I use the elimination method I get x and y to equal 0.

Is this correct and does this mean it has infinitely many solutions?

2x + 3y = 1

4x + 6y = 2

For some reason when I use the elimination method I get x and y to equal 0.

Is this correct and does this mean it has infinitely many solutions?

2x + 3y = 1---->- 4x - 6y = -2 {multiplied top equation by -2}

4x + 6y = 2------>4x + 6y = 2

when the new equations are added together you get:

0 = 0

if the variables disappear and you get a statement that is always true,

there are infinite solutions {meaning these two equations represent the same line}

Additional Note:

if the variables disappear and you get a statement that is never true, then there is no solution

{meaning the lines would not cross or they are parallel lines}

- Algebra House

4x + 6y = 2------>4x + 6y = 2

when the new equations are added together you get:

0 = 0

if the variables disappear and you get a statement that is always true,

there are infinite solutions {meaning these two equations represent the same line}

Additional Note:

if the variables disappear and you get a statement that is never true, then there is no solution

{meaning the lines would not cross or they are parallel lines}

- Algebra House