Solving Equations Using Substitution Quick Check

Question

1 of 51 of 5 Items
Question
Solve the system of two equations using substitution.
y=2+3x

4x−3y=−16
(1 point)
Responses

(−2, −4)
left parenthesis negative 2 comma negative 4 right parenthesis

(2, 10)
left parenthesis 2 comma 10 right parenthesis

(−2, 4)
left parenthesis negative 2 comma 4 right parenthesis

(2, 8)

Answer 1

To solve the system of equations using substitution, we have the following equations:

1. \(y = 2 + 3x\)
2. \(4x - 3y = -16\)

We can substitute the expression for \(y\) from the first equation into the second equation.

Substituting \(y = 2 + 3x\) into the second equation gives us:

\[ 4x - 3(2 + 3x) = -16 \]

Now, simplify the equation:

\[ 4x - 6 - 9x = -16 \]

Combine like terms:

\[ -5x - 6 = -16 \]

Next, add 6 to both sides:

\[ -5x = -10 \]

Now, divide both sides by -5:

\[ x = 2 \]

Now that we have \(x\), we can substitute it back into the first equation to find \(y\):

\[ y = 2 + 3(2) = 2 + 6 = 8 \]

Thus, the solution to the system of equations is \((x, y) = (2, 8)\).

So the correct response is:

\((2, 8)\)