Question

10x − 8y = 16
5x − 3y = 1

Answer 1

To solve the system of equations:

1. **Equation 1**: \(10x - 8y = 16\)
2. **Equation 2**: \(5x - 3y = 1\)

We can use the method of substitution or elimination. Here, I'll use the elimination method.

First, let's simplify Equation 1 by dividing all terms by 2:

\[
5x - 4y = 8 \quad \text{(Equation 3)}
\]

Now we have the following two equations:

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

Next, we'll eliminate \(5x\) by subtracting Equation 2 from Equation 3:

\[
(5x - 4y) - (5x - 3y) = 8 - 1
\]

This simplifies to:

\[
-4y + 3y = 7
\]

or

\[
-y = 7
\]

Thus, we find:

\[
y = -7
\]

Now that we have \(y\), we can substitute it back into either of the original equations to find \(x\). Let's use Equation 2 for this purpose:

\[
5x - 3(-7) = 1
\]

This simplifies to:

\[
5x + 21 = 1
\]

Subtracting 21 from both sides gives us:

\[
5x = 1 - 21
\]
\[
5x = -20
\]

Dividing both sides by 5:

\[
x = -4
\]

Thus, the solution to the system of equations is:

\[
\boxed{(x, y) = (-4, -7)}
\]