Solve the system of equations by substitution.
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 ∅.
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)}.
To solve the system of equations by substitution, we can substitute the expression for y from the second equation into the first equation.
Given:
2x + y = 12,
y = 4x.
Substitute y = 4x into the first equation:
2x + 4x = 12.
Combine like terms:
6x = 12.
Divide both sides by 6:
x = 2.
Now, substitute the value of x back into the second equation to find y:
y = 4(2) = 8.
Therefore, the solution to the system of equations is the ordered pair (x, y) = (2, 8).
Taking the answer choices into consideration, the correct choice is:
A. There are a finite number of solutions. The solution set is {(2, 8)}
To solve the system of equations by substitution, we will substitute the value of y from the second equation into the first equation.
Given:
1) 2x + y = 12
2) y = 4x
Now, substitute the value of y from equation 2 into equation 1:
2x + (4x) = 12
Combine like terms:
6x = 12
Divide both sides by 6 to solve for x:
x = 2
Now, substitute the value of x back into equation 2 to find the value of y:
y = 4(2)
y = 8
Therefore, the solution to the system of equations is x = 2 and y = 8.
So, the correct choice is A. There are a finite number of solutions. The solution set is (2, 8).