Solve the system of two equations using substitution. y=2+3x 4x−3y=−16 (1 point) Responses (−2, 4) left parenthesis negative 2 comma 4 right parenthesis (2, 10) left parenthesis 2 comma 10 right parenthesis (2, 8) left parenthesis 2 comma 8 right parenthesis (−2, −4)

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.

Step 1: Substitute for \( y \)

Substituting \( y \) in the second equation:

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

Step 2: Distribute the \(-3\)

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

Step 3: Combine like terms

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

Step 4: Add 6 to both sides

\[ -5x = -10 \]

Step 5: Divide by -5

\[ x = 2 \]

Step 6: Substitute \( x \) back into the first equation to find \( y \)

Now we substitute \( x = 2 \) back into the first equation:

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

\[ y = 2 + 6 = 8 \]

Step 7: Write the solution as an ordered pair

The solution to the system of equations is:

\[ (x, y) = (2, 8) \]

So the answer is \( (2, 8) \).