Question

Solve the system of linear equations. Y=-1/6x+5 and x+6y=30 Can you explain the steps?

Answer 1

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.

• x + 6(-1/6x + 5) = 30

Distribute 6 inside the parentheses.

• x - x + 30 = 30

Combine like terms.

• 30 = 30

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.