The problem is to solve the following system of equations: $2x + 8y = 120$ $x = 60 - 4y$

1. Problem Description

The problem is to solve the following system of equations:

$2x + 8y = 120$

$x = 60 - 4y$

2. Solution Steps

We can use substitution to solve this system of equations.

Substitute the expression for $x$ from the second equation into the first equation:

$2(60 - 4y) + 8y = 120$

Expand the expression:

$120 - 8y + 8y = 120$

Simplify the equation:

$120 = 120$

Since $120 = 120$ is always true, this system has infinitely many solutions. The two equations are dependent.

We can rewrite the first equation by dividing by 2:

$x + 4y = 60$

$x = 60 - 4y$

This confirms that the two equations are equivalent.

We can express the solution in terms of a parameter. Let $y = t$. Then $x = 60 - 4t$.

The solution set is $\{(60-4t, t) | t \in \mathbb{R}\}$.

3. Final Answer

The system has infinitely many solutions of the form $x = 60 - 4y$.