Simultaneous equation 4x-3y=23 and 2x-5y=8

To solve the system of simultaneous equations:

1) \( 4x - 3y = 23 \)
2) \( 2x - 5y = 8 \)

We'll use the method of elimination. Here's the process:

### Step 1: Multiply both equations to eliminate one variable.
We aim to eliminate \( x \). To do that, multiply equation (2) by 2 so the coefficients of \( x \) match.

- Equation (1): \( 4x - 3y = 23 \)
- Equation (2) (multiplied by 2): \( 4x - 10y = 16 \)

### Step 2: Subtract equation (2) from equation (1).
\[
(4x - 3y) - (4x - 10y) = 23 - 16
\]
This simplifies to:
\[
7y = 7
\]

### Step 3: Solve for \( y \).
\[
y = \frac{7}{7} = 1
\]

### Step 4: Substitute \( y = 1 \) into one of the original equations to solve for \( x \).
We'll use equation (2):
\[
2x - 5(1) = 8
\]
\[
2x - 5 = 8
\]
\[
2x = 13
\]
\[
x = \frac{13}{2} = 6.5
\]

### Solution:
The solution to the system is:
\[
x = 6.5, \quad y = 1
\]

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Learn how to solve the system of simultaneous equations 4x - 3y = 23 and 2x - 5y = 8 using the elimination method. This detailed step-by-step solution covers key algebraic concepts, such as elimination and substitution, and is suitable for students in Grades 9-10.

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