To determine which system will produce infinitely many solutions, we need to check if the two equations are equivalent or proportional.
Looking at the systems of equations given:
1) −6x + 3y = 18
4x − 3y = 6
The equations are not equivalent or proportional.
2) 2x + 4y = 24
6x + 12y = 36
The second equation is three times the first equation, so they are proportional and will have infinitely many solutions.
3) 3x − y = 14
−9x + 3y = −42
The equations are not equivalent or proportional.
4) 5x + 2y = 13
−x + 4y = −6
The equations are not equivalent or proportional.
Therefore, the system of equations 2) 2x + 4y = 24 and 6x + 12y = 36 will produce infinitely many solutions.
Determine which system will produce infinitely many solutions.
−6x + 3y = 18
4x − 3y = 6
2x + 4y = 24
6x + 12y = 36
3x − y = 14
−9x + 3y = −42
5x + 2y = 13
−x + 4y = −6
1 answer