Question

One solution, infinitely many solutions, or no solution for #13?

Answer 1

Answer:

For this system of equations there is infinitely many solutions.  

Step-by-step explanation:

Given the equations:  -4x + 4y = 32 and 3x + 24 = 3y, we need to first get them both in standard form (Ax + By = C) in order to complete the method of elimination to solve.  The first equatoin is already in standard form, however, in order to convert the second equation, we will need to use inverse operations to move the '3x' to the other side of the equation by subtraction of this term from both sides:  3x - 3x + 24 = 3y - 3x or 24 = -3x + 3y.  Rearranging the equation gives us:  -3x + 3y = 24.  In order to use elimination to solve, we must first multiply the first equation be a factor of 3 and the second equation by a factor of -4 in order to have opposite coefficients:

3[ -4x + 4y = 32] = -12x + 12y = 96

-4{-3x + 3y = 24] = 12x - 12y = -96

You can see that if we add these too equations together, we get 0 = 0, which indicates that they are both the same line, making our answer infinitely many solutions.  

Answer 2

Answer:

all work is ahown/pictured