Question

how many solutions does the system of equations have 3x=-12y+15 and x+4y=5

Answer 1

To find the number of solutions, we can solve this system of equations using any method (substitution, elimination, or graphing).

Let's solve it using the elimination method:

Multiply the first equation by 4 to make the coefficients of y in both equations the same:

12x = -48y + 60
x + 4y = 5

Now, subtract the second equation from the first:

(12x - x) = (-48y + 60) - 4y
11x = -52y + 60

Simplify:

11x + 52y = 60

Now we have a linear equation in the form ax + by = c. This equation represents the same line as the second equation.

Since the two equations represent the same line, they are redundant and have infinite solutions.