Question

Muriel says she has written a system of two linear equations that has an infinite number of solutions. One of the equations of the system is 3y = 2x – 9. Which could be the other equation?
2y = x – 4.5
y = x – 3
6y = 6x – 27
y = x – 4.5

Answer 1

The choices from other sources are as follows: 2y = x – 4.5 y = 2/3x – 3 6y = 6x – 27 y = 3/2x – 4.5 For a system of two linear equations to have infinite solutions, all of the points lie on the same graph for both equations. Mathematically, we can quickly check that using the equation's general form. If the ratio of the values of their corresponding cofficients are equal, then they have infinite solutions. For example, 3y - 2x = -9 and 2y -x = -4.5| The ratio of their coefficients for y is 3/2 and that for x is -2/-1 = 2. This clearly shows that the corresponding coefficients do not have the same ratio. We do this for the rest of the choices and find that for 3y - 2x = -9 and y - 2/3x = -3| The ratios of the coefficients are as follows: 3/1,-2/(-2/3), and (-9)/(-3). All of which are equal to 3. Thus, the two have infinite solutions. Therefore the answer is B: y = 2/3x - 3.

Answer 2

Answer: B

Step-by-step explanation: