Solve the system by using the substitution method.
{(y = 3/5 x - 5, 5 x - 8 y = 43)
{(x, y)} = {(   ,   )}

To solve the system of equations using the substitution method, follow these steps:

### System of equations:
1. \( y = \frac{3}{5}x - 5 \) (Equation 1)
2. \( 5x - 8y = 43 \) (Equation 2)

### Step 1: Substitute \( y \) from Equation 1 into Equation 2.
From Equation 1, we know \( y = \frac{3}{5}x - 5 \). Now, substitute this expression for \( y \) in Equation 2:

\[
5x - 8\left( \frac{3}{5}x - 5 \right) = 43
\]

### Step 2: Distribute and simplify.
Distribute \( -8 \) over \( \left( \frac{3}{5}x - 5 \right) \):

\[
5x - 8\left( \frac{3}{5}x \right) + 8(5) = 43
\]

\[
5x - \frac{24}{5}x + 40 = 43
\]

### Step 3: Eliminate the fraction.
To eliminate the fraction, multiply the entire equation by 5:

\[
5(5x) - 5\left( \frac{24}{5}x \right) + 5(40) = 5(43)
\]

This simplifies to:

\[
25x - 24x + 200 = 215
\]

### Step 4: Combine like terms.
Now, combine the like terms:

\[
x + 200 = 215
\]

### Step 5: Solve for \( x \).
Subtract 200 from both sides:

\[
x = 215 - 200
\]

\[
x = 15
\]

### Step 6: Substitute \( x = 15 \) into Equation 1 to find \( y \).
Now that we know \( x = 15 \), substitute this value into Equation 1:

\[
y = \frac{3}{5}(15) - 5
\]

\[
y = 9 - 5
\]

\[
y = 4
\]

### Final solution:
The solution to the system of equations is:
\[
(x, y) = (15, 4)
\]

Would you like further clarification on any part of this process?

Here are 5 related questions to expand your understanding:
1. How do you handle a system of equations that results in no solution?
2. Can the substitution method be used for non-linear systems of equations?
3. How would you solve a system of equations using the elimination method instead?
4. What are the advantages of the substitution method over graphing?
5. How does the substitution method compare to solving systems by matrices?

**Tip:** Always check your solution by substituting the values of \( x \) and \( y \) into both original equations to verify accuracy.

Solve the system by using the substitution method. {(y = 3/5 x - 5, 5 x - 8 y = 43) {(x, y)} = {(   ,   )}

Learn how to solve a system of linear equations using the substitution method. This example uses the equations y = (3/5)x - 5 and 5x - 8y = 43. The step-by-step solution demonstrates algebraic techniques such as substitution, distribution, and combining like terms. Suitable for students in Grades 9-11.

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