solve these 2 equations 
1.263x + 1.64y + 75 = 110.68 
7.047x - 5.33568y + 5 = 0

We are given the following system of two equations:

1. \( 1.263x + 1.64y + 75 = 110.68 \)
2. \( 7.047x - 5.33568y + 5 = 0 \)

We will solve this system using substitution or elimination.

### Step 1: Simplify both equations

**Equation 1**:
\[
1.263x + 1.64y = 110.68 - 75 \implies 1.263x + 1.64y = 35.68
\]
 
**Equation 2**:
\[
7.047x - 5.33568y = -5
\]

### Step 2: Solve one equation for one variable

Let's solve the first equation for \( x \):
\[
1.263x = 35.68 - 1.64y
\]
\[
x = \frac{35.68 - 1.64y}{1.263}
\]

### Step 3: Substitute into the second equation

Now substitute this expression for \( x \) into the second equation:
\[
7.047\left(\frac{35.68 - 1.64y}{1.263}\right) - 5.33568y = -5
\]
Simplify this equation to solve for \( y \).The solution to the system of equations is:

\[
x \approx 9.96, \quad y \approx 14.09
\]

If you'd like further details or have any questions, feel free to ask.

Here are 5 related questions:
1. How do we solve a system of linear equations using the substitution method?
2. What are other methods for solving systems of equations (e.g., elimination, matrix methods)?
3. How can systems of equations be solved using matrices (Gaussian elimination)?
4. What happens when a system of equations has no solutions or infinitely many solutions?
5. How can we check if the solution is correct?

**Tip**: Always simplify equations as much as possible before attempting to solve them—it makes calculations easier!

solve these 2 equations 1.263x + 1.64y + 75 = 110.68 7.047x - 5.33568y + 5 = 0

This guide provides a step-by-step solution to a system of two linear equations: 1.263x + 1.64y + 75 = 110.68 and 7.047x - 5.33568y + 5 = 0. Learn how to apply the substitution method to solve for x and y, with simplified steps and clear explanations. Suitable for high school students in Grades 10-12.

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