Question

Which ordered pair is the solution to the system below?

5x+3y=29

2x−y=5

Answer 1

To solve the system of equations, we have:

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

We can use the substitution or elimination method to find the values of \( x \) and \( y \).

Let's use the substitution method. First, we can solve Equation 2 for \( y \):

\[
y = 2x - 5
\]

Now, we substitute this expression for \( y \) into Equation 1:

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

Expanding this:

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

Combine like terms:

\[
11x - 15 = 29
\]

Next, add 15 to both sides:

\[
11x = 44
\]

Now, divide by 11:

\[
x = 4
\]

Now that we have \( x \), we can substitute it back into the expression we found for \( y \):

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

So, the solution to the system of equations is the ordered pair:

\[
(4, 3)
\]

To verify, we can plug \( x = 4 \) and \( y = 3 \) back into both original equations:

For Equation 1:

\[
5(4) + 3(3) = 20 + 9 = 29 \quad \text{(True)}
\]

For Equation 2:

\[
2(4) - 3 = 8 - 3 = 5 \quad \text{(True)}
\]

Both equations are satisfied, thus confirming that the solution is correct.

The final answer is:

\((4, 3)\)