Solve the system of equations by substitution.

Question

2x+y
=
12
y
=
4x
.
.
.
Question content area right
Part 1
Select the correct choice below​ and, if​ necessary, fill in the answer box to complete your choice.
A.
There are a finite number of solutions. The solution set is enter your response here.
​(Simplify your answer. Type an ordered​ pair.)
B.
There are infinitely many solutions. The solution set is x,enter your response here.
​(Simplify your answer. Type an expression in terms of​ x.)
C.
The solution set is ∅.

Answer 1

To solve the system of equations by substitution, we can substitute the value of y from the second equation into the first equation.

Given that y = 4x, we can substitute this value into the first equation:

2x + (4x) = 12

Simplifying this equation, we get:

6x = 12

Dividing both sides of the equation by 6, we find:

x = 2

Now that we have the value of x, we can substitute it back into the second equation to find the value of y:

y = 4(2)

y = 8

Therefore, the solution to the system of equations is the ordered pair (2, 8).

The correct choice is:

A. There are a finite number of solutions. The solution set is {(2, 8)}.