Question

Solve the system of equations
{ 3x +2y =15
{ 5x -4y=-8

The ________ method was used to solve the system.
Responses
A elimination
B substitution
C graphing

What was the solution to the system?
Responses
A (9/2, 2)
B (2, 9/2)

Answer 1

To solve the given system of equations:

1. \( 3x + 2y = 15 \) (Equation 1)
2. \( 5x - 4y = -8 \) (Equation 2)

Let's use the elimination method to solve for \(x\) and \(y\).

First, we can multiply Equation 1 by 2 in order to align the \(y\) coefficients:

\[
2(3x + 2y) = 2(15) \implies 6x + 4y = 30 \quad (Equation 3)
\]

Now we have:
- Equation 3: \( 6x + 4y = 30 \)
- Equation 2: \( 5x - 4y = -8 \)

Next, we can add Equation 3 and Equation 2:

\[
(6x + 4y) + (5x - 4y) = 30 + (-8)
\]
\[
6x + 4y + 5x - 4y = 30 - 8
\]
\[
11x = 22
\]

Now we solve for \(x\):

\[
x = \frac{22}{11} = 2
\]

Next, we substitute \(x = 2\) back into Equation 1 to find \(y\):

\[
3(2) + 2y = 15
\]
\[
6 + 2y = 15
\]
\[
2y = 15 - 6
\]
\[
2y = 9
\]
\[
y = \frac{9}{2}
\]

The solution to the system of equations is \( (2, \frac{9}{2}) \).

Thus, the answers to the questions are:
- The **elimination** method was used to solve the system. (Response A)
- The solution to the system is \( (2, \frac{9}{2}) \). (Response B)