Question

solve the system of linear equations by substitution. enter your answer as an ordered pair if the system has a solution. otherwise, enter \all real numbers\ if it has infinite solutions or
o solution\ if it has no solutions. \\(\

$$\begin{cases} x + 4y = -4 \\\\ 5x + 20y = -20 \\end{cases}$$

\\)

Explanation:

Step1: Solve first equation for x

From \( x + 4y = -4 \), we get \( x = -4 - 4y \).

Step2: Substitute x into second equation

Substitute \( x = -4 - 4y \) into \( 5x + 20y = -20 \):
\( 5(-4 - 4y) + 20y = -20 \)

Step3: Simplify the equation

Expand: \( -20 - 20y + 20y = -20 \)
Combine like terms: \( -20 = -20 \)
This is a true statement, meaning the two equations are dependent (represent the same line), so there are infinite solutions.

Answer:

all real numbers