To find four solutions for the equation [tex]\( 12x + 5y = 0 \)[/tex], we can proceed as follows:
1. Identify the equation:
[tex]\[
12x + 5y = 0
\][/tex]
2. Rearrange the equation to solve for [tex]\( y \)[/tex] in terms of [tex]\( x \)[/tex]:
[tex]\[
5y = -12x
\][/tex]
[tex]\[
y = -\frac{12}{5}x
\][/tex]
3. Choose different values for [tex]\( x \)[/tex] and use the rearranged equation to solve for the corresponding [tex]\( y \)[/tex] values:
- For [tex]\( x = 1 \)[/tex]:
[tex]\[
y = -\frac{12}{5} \cdot 1 = -\frac{12}{5} = -2.4
\][/tex]
So, one solution is [tex]\( (1, -2.4) \)[/tex].
- For [tex]\( x = -1 \)[/tex]:
[tex]\[
y = -\frac{12}{5} \cdot (-1) = \frac{12}{5} = 2.4
\][/tex]
So, another solution is [tex]\( (-1, 2.4) \)[/tex].
- For [tex]\( x = 2 \)[/tex]:
[tex]\[
y = -\frac{12}{5} \cdot 2 = -\frac{24}{5} = -4.8
\][/tex]
So, another solution is [tex]\( (2, -4.8) \)[/tex].
- For [tex]\( x = -2 \)[/tex]:
[tex]\[
y = -\frac{12}{5} \cdot (-2) = \frac{24}{5} = 4.8
\][/tex]
So, another solution is [tex]\( (-2, 4.8) \)[/tex].
4. Summarize the solutions:
The four solutions to the equation [tex]\( 12x + 5y = 0 \)[/tex] are:
[tex]\[
(1, -2.4), (-1, 2.4), (2, -4.8), (-2, 4.8)
\][/tex]
