To solve the system of linear equations:

\[ 
4x + 5y = 23 \quad (1)
\]
\[ 
2x - 3y = -1 \quad (2)
\]

we can use either the substitution method or the elimination method. Here, I'll use the elimination method.

**Step 1: Align the equations:**

\[ 
4x + 5y = 23 \quad (1)
\]
\[ 
2x - 3y = -1 \quad (2)
\]

**Step 2: Make the coefficients of \( x \) or \( y \) equal:**

Multiply equation (2) by 2 so that the coefficient of \( x \) in both equations becomes the same:

\[ 
4x + 5y = 23 \quad (1)
\]
\[ 
4x - 6y = -2 \quad (3)
\]

**Step 3: Subtract equation (3) from equation (1):**

\[ 
(4x + 5y) - (4x - 6y) = 23 - (-2)
\]
\[ 
4x + 5y - 4x + 6y = 23 + 2
\]
\[ 
11y = 25
\]
\[ 
y = \frac{25}{11}
\]

**Step 4: Substitute \( y \) back into one of the original equations to solve for \( x \):**

Substitute \( y = \frac{25}{11} \) into equation (2):

\[ 
2x - 3\left(\frac{25}{11}\right) = -1
\]
\[ 
2x - \frac{75}{11} = -1
\]
\[ 
2x = -1 + \frac{75}{11}
\]
\[ 
2x = \frac{-11 + 75}{11}
\]
\[ 
2x = \frac{64}{11}
\]
\[ 
x = \frac{32}{11}
\]

So, the solution to the system of equations is:

\[ 
x = \frac{32}{11}, \quad y = \frac{25}{11}
\]

Would you like more details or have any questions?

---

Here are some related questions for further practice:

1. Solve the system of equations using the substitution method: \(3x + 4y = 17\) and \(x - 2y = -3\).
2. Find the solution to the system: \(5x + 2y = 8\) and \(3x - 4y = -14\).
3. Determine \(x\) and \(y\) for the equations: \(x + y = 10\) and \(2x - y = 3\).
4. Solve the system: \(7x + 3y = 1\) and \(x - y = 4\).
5. Use elimination to solve: \(2x + 5y = 16\) and \(4x - 10y = -8\).
6. Solve by substitution: \(x + 2y = 6\) and \(4x - y = 5\).
7. Determine the solution: \(3x - y = 7\) and \(x + 2y = 4\).
8. Solve using any method: \(6x + y = 19\) and \(2x - 3y = -7\).

**Tip:** When solving systems of equations, it's often useful to double-check your solutions by substituting them back into the original equations to ensure they satisfy both equations.

Learn how to solve the system of linear equations 4x + 5y = 23 and 2x - 3y = -1 step-by-step using the elimination method. This problem involves key algebraic concepts such as systems of linear equations and the elimination method. Suitable for high school students.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation