Select the correct solution for this pair of simultaneous equations:

3x+2y=9

5x−4y=4

Select one:

x=2
, y=3


x=2
, y=1.5


x=1411
, y=5722


x=14
, y=−332

To solve the pair of simultaneous equations:

\[
3x + 2y = 9
\]
\[
5x - 4y = 4
\]

Let's solve these equations step by step using the substitution or elimination method. We'll use the elimination method here:

1. **Multiply the first equation by 2** to make the coefficients of \( y \) the same:

\[
2(3x + 2y) = 2(9)
\]
\[
6x + 4y = 18
\]

2. **Add the new equation to the second equation** to eliminate \( y \):

\[
(6x + 4y) + (5x - 4y) = 18 + 4
\]
\[
11x = 22
\]

3. **Solve for \( x \)**:

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

4. **Substitute \( x = 2 \) into the first equation** to find \( y \):

\[
3(2) + 2y = 9
\]
\[
6 + 2y = 9
\]
\[
2y = 3
\]
\[
y = \frac{3}{2} = 1.5
\]

Thus, the correct solution is \( x = 2 \) and \( y = 1.5 \).

The correct answer is:

**x = 2, y = 1.5**

---

Would you like a detailed explanation, or do you have any questions? Here are some related problems you might consider:

1. Solve the system of equations using substitution.
2. What is the determinant of the coefficient matrix for this system?
3. How would the solution change if the first equation was \( 3x + 2y = 8 \)?
4. Can these equations be solved graphically? What would their intersection point represent?
5. How can you check if the solution is correct?

**Tip:** When solving simultaneous equations, always check your solution by substituting the values back into the original equations.

Learn how to solve the pair of simultaneous equations 3x + 2y = 9 and 5x - 4y = 4 step-by-step using the elimination method. Includes detailed solution and explanation suitable for high school students. Solve for x and y with clear, guided steps.

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