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egin{ $-20$ x+ $12$ y= $24$ } and egin{ $-5$ x+ $2$ y=rac{ $6$ }{}} consider the system of equations. how many egin{(x,y)} solutions does this system have?

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Write and solve direct variation equations

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Q. egin{

-20

x+

12

y=

24

} and egin{

-5

x+

2

y=rac{

6

}{}} consider the system of equations. how many egin{(x,y)} solutions does this system have?

Analyze Equations: Analyze the system of equations to determine if they are multiples of each other. $\newline$ The system of equations is: $\newline$ $-20x + 12y = 24$ $\newline$ $-5x + 2y = 6$ $\newline$ We can simplify the first equation by dividing all terms by $4$ : $\newline$ $-20x/4 + 12y/4 = 24/4$ $\newline$ $-5x + 3y = 6$ $\newline$ Now, compare the simplified first equation with the second equation: $\newline$ $-5x + 3y = 6$ $\newline$ $-5x + 2y = 6$ $\newline$ We can see that the coefficients of $x$ are the same in both equations, but the coefficients of $y$ and the constants are different.
Simplify First Equation: Since the coefficients of $x$ are the same but the coefficients of $y$ and the constants are different, we can conclude that the lines represented by these equations are parallel. $\newline$ Parallel lines never intersect, which means there are no points $(x, y)$ that satisfy both equations simultaneously.

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