Solve the Equation: Use Substitution for 8x - 2y = 10 and 3x + 3y = 9

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

• Solve $3x + 3y = 9$ for $y$:

Divide the whole equation by 3 to simplify:
$x + y = 3$

• Express $y$ in terms of $x$:

$y = 3 - x$

• Substitute $y = 3 - x$ into the first equation:

We substitute into $8x - 2y = 10$:
$8x - 2(3 - x) = 10$

Simplify and solve for $x$:

$8x - 6 + 2x = 10$
$10x - 6 = 10$
Add 6 to both sides:
$10x = 16$
Divide by 10:
$x = \frac{16}{10} = \frac{8}{5}$

• Substitute back to find $y$:

Use $y = 3 - x$:
$y = 3 - \frac{8}{5} = \frac{15}{5} - \frac{8}{5} = \frac{7}{5}$

Therefore, the solution to the system is $x = \frac{8}{5}$ and $y = \frac{7}{5}$.