Answer:
Infinitely many solutions
Step-by-step explanation:
y = -1/6x + 5
x + 6y = 30
We can solve this system by using substitution or elimination. Since we are given an isolated y-value, I'll be using the substitution method.
Substitute y = -1/6x + 5 into the second equation for y.
Distribute 6 inside the parentheses.
Combine like terms.
Since this is a true statement, we can conclude that this system has a solution of all real numbers, or infinitely many solutions.
We can also see that these equations are indeed equivalent by multiplying the top equation by 6.
6 * (y = -1/6x + 5) → 6y = -x + 30
Adding x to both sides and rearranging terms gives us x + 6y = 30, which is the same as the second equation.
