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y=2+3x

4x−3y=−16
(1 point)
Responses

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

(2, 8)
left parenthesis 2 comma 8 right parenthesis

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

(−2, −4)

1 answer

To find the solution to the system of equations given, we can substitute the expression for \(y\) from the first equation into the second equation.

  1. The first equation is:
    \[ y = 2 + 3x \]

  2. The second equation is:
    \[ 4x - 3y = -16 \]

Now, we can substitute the expression for \(y\) into the second equation:

Substituting \(y\) in the second equation: \[ 4x - 3(2 + 3x) = -16 \]

Distributing the \(-3\): \[ 4x - 6 - 9x = -16 \]

Combining like terms: \[ -5x - 6 = -16 \]

Now, add \(6\) to both sides: \[ -5x = -10 \]

Dividing by \(-5\): \[ x = 2 \]

Now, we can find \(y\) using the value of \(x\): \[ y = 2 + 3(2) = 2 + 6 = 8 \]

So, the solution to the system is: \[ (x, y) = (2, 8) \]

Therefore, the correct answer is: \[ \text{(2, 8)} \]