Question

Determine whether the linear system has one solution no solution or infinitely many solutions

3x + y = 12
Y = 3x + 12​

Answer 1

Explanation:

We can solve the system by substitution. Since the second equation is already solved for y, we can substitute 3x + 12 for y in the first equation and get:

3x + (3x + 12) = 12

Simplifying this equation, we get:

6x + 12 = 12

Subtracting 12 from both sides, we get:

6x = 0

Dividing both sides by 6, we get:

x = 0

Now that we know x, we can substitute it into either equation to find y. Using the second equation, we get:

y = 3(0) + 12 = 12

Therefore, the solution to the system is (x,y) = (0,12).

Since there is only one solution, the system has one solution.