The problem asks to find the number of solutions to the given system of equations: $y = -4x + 3$ $2x + 8y = 10$

1. Problem Description

The problem asks to find the number of solutions to the given system of equations:

$y = -4x + 3$

$2x + 8y = 10$

2. Solution Steps

We can substitute the first equation into the second equation to solve for $x$.

$2x + 8(-4x + 3) = 10$

$2x - 32x + 24 = 10$

$-30x = 10 - 24$

$-30x = -14$

$x = \frac{-14}{-30} = \frac{7}{15}$

Now, substitute $x = \frac{7}{15}$ back into the first equation to find $y$:

$y = -4(\frac{7}{15}) + 3$

$y = -\frac{28}{15} + 3$

$y = -\frac{28}{15} + \frac{45}{15}$

$y = \frac{17}{15}$

Since we found a unique solution for $x$ and $y$, the system has one solution.

3. Final Answer

The system of equations has one solution.