Question

Question 1
Which ordered pair is the solution to the system below?

5x+3y=29

2x−y=5

Answer 1

To find the ordered pair (x, y) that is the solution to the system of equations:

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

We can solve this system using the substitution or elimination method. Here we'll use the substitution method:

First, solve Equation 2 for \(y\):

\[
2x - y = 5
\]
Rearranging gives:
\[
y = 2x - 5
\]

Now substitute this expression for \(y\) in Equation 1:

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

Now simplify and solve for \(x\):

\[
5x + 6x - 15 = 29
\]
\[
11x - 15 = 29
\]
\[
11x = 29 + 15
\]
\[
11x = 44
\]
\[
x = 4
\]

Now substitute \(x = 4\) back into the equation for \(y\):

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

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

So the solution is:
\[
\boxed{(4, 3)}
\]