how many solutions does y = 3x + 6 y = -13x - 4 have

Answer 1

To determine the number of solutions for the system of equations y = 3x + 6 and y = -13x - 4, we can solve the system by setting the two equations equal to each other:

3x + 6 = -13x - 4

Now, we solve for x:

3x + 13x = -4 - 6
16x = -10
x = -10/16
x = -5/8

Now, substitute this value of x back into either equation to find the corresponding y-value. Using y = 3x + 6:

y = 3(-5/8) + 6
y = -15/8 + 48/8
y = 33/8

Therefore, the system has one solution: (-5/8, 33/8).