Question

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).**