Question

K

Solve the system of equations by substitution.
2x + y = 6
y = 4x
Points: 0 of 1
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Select the correct choice below and, if necessary,
fill in the answer box to complete your choice.
OA.
There are a finite number of solutions. The
solution set is
(Simplify your answer. Type an
ordered pair.)
B. There are infinitely many solutions. The
solution set is {(x)}.
(Simplify your answer. Type an expression
in terms of x.)
OC. The solution set is Ø.

Answer 1

Substitute y = 4x into the first equation:

2x + 4x = 6

Simplifying, we get:

6x = 6

Dividing by 6, we get:

x = 1

Substituting x = 1 into y = 4x, we get:

y = 4(1)

y = 4

So, the solution is (1, 4), and there is a unique solution to the system of equations.

The answer is OA. The solution set is (1, 4).

Answer 2

The solution set is (1, 4)
There are a finite number of solutions.

Explanation:

We have 2x+y=6 and y=4x.

Let's write the first equation into y=mx+b form.

We get: y=-2x+6

Now, we just set the equations equal to each other.

-2x+6=4x Add 2x to both sides.

6=6x Divide both sides by 6

x=1

Now, plug x back into either of the equations given to us.

y=4(1)

y=4

The solution set is (1, 4)