Which ordered pair is the solution to the system below? 5x+3y=29 2x−y=5 (1 point) Responses (4,3) (4,3) (3,4) (3,4)

Answer 1

To find the solution to the system of equations given:

1. \( 5x + 3y = 29 \) (Equation 1)
2. \( 2x - y = 5 \) (Equation 2)

We can solve this using substitution or elimination. We'll use substitution here.

First, let's solve Equation 2 for \(y\):

\[ 2x - y = 5 \implies y = 2x - 5 \]

Next, we'll substitute \(y\) in Equation 1:

\[ 5x + 3(2x - 5) = 29 \]

Now, simplify the equation:

\[ 5x + 6x - 15 = 29 \]

Combine like terms:

\[ 11x - 15 = 29 \]

Add 15 to both sides:

\[ 11x = 44 \]

Now, divide by 11:

\[ x = 4 \]

Next, substitute \(x = 4\) back into the expression for \(y\):

\[ y = 2(4) - 5 = 8 - 5 = 3 \]

Thus, the solution to the system is \((4, 3)\).

The correct ordered pair is (4, 3).