Question

medium
solve each system of equations by substitution.
$y = -4x + 1$
$-12x - 3y = -3$
please do not write on these. they will be used in
classes.

Explanation:

Step1: Substitute \( y = -4x + 1 \) into the second equation

We have the second equation \( -12x - 3y = -3 \). Substitute \( y \) with \( -4x + 1 \):
\( -12x - 3(-4x + 1) = -3 \)

Step2: Simplify the equation

First, distribute the -3: \( -12x + 12x - 3 = -3 \)
Then, combine like terms: \( (-12x + 12x) - 3 = -3 \) which simplifies to \( 0x - 3 = -3 \) or \( -3 = -3 \)

This is a true statement, which means the two equations represent the same line, so there are infinitely many solutions. The solution set can be written as \( \{(x, y) | y = -4x + 1\} \) (all points on the line \( y = -4x + 1 \)).

Answer:

There are infinitely many solutions, and the solution set is \( \{(x, y) | y = -4x + 1\} \)