Question

From the list of equations: 1. y=x-3 2. y=2x-6 3. 3y=3x-9 4. 3y=3x 9 Which pair of equations forms a system that has infinitely many solutions?

Answer 1

To find a system with infinitely many solutions, we compare the slopes and y-intercepts of the equations. One pair that satisfies this is y = x - 3 and 3y = 3x - 9.

Step-by-step explanation:

To determine which pair of equations forms a system with infinitely many solutions, we need to check if the slopes and y-intercepts of the equations are equal.

Let's compare the equations:

1. y = x - 3 (slope = 1, y-intercept = -3)
2. y = 2x - 6 (slope = 2, y-intercept = -6)
3. 3y = 3x - 9 (slope = 1, y-intercept = -3)
4. 3y = 3x + 9 (slope = 1, y-intercept = 3)

The pair of equations that has the same slope and y-intercept is:

1. y = x - 3
2. 3y = 3x - 9

Therefore, the pair of equations that forms a system with infinitely many solutions is y = x - 3 and 3y = 3x - 9.