Assuming your system of equations is
[tex]\begin{cases}-5.9 x-3.7 y = -2.1\\ 5.9 x + 3.7 y = 2.1\end{cases}[/tex]
The answer is C. Infinitely many solutions. If my assumption is incorrect, then the answer will be likely different.
The reason why it's "infinitely many solutions" is because the first equation is the same as the second equation. The only difference is that everything was multiplied by -1. You could say that both sides were multiplied by -1.
Both equations given graph out the same line. They overlap perfectly yielding infinitely many solution points on the line.
Option C is correct. The system of linear equation -5.9x - 3.7y = -2.1 and 5.9x +3.7y = 2.1 have infinitely many solutions.
The system of linear equations is "a set of two or more linear equations or variables is called system of linear equation".
An equation has infinitely many solutions only if "the two lines are coincident and having the same y-intercept".
According to the question,
The system of linear equation,
-5.9 x - 3.7y = -2.1 → (1)
5.9 x + 3.7y = 2.1 → (2)
The equation (1) is same as the equation (2) only the difference equation (1) is multiplied by (-1). Both equation give the same line. To check if above equations have same y-intercept, the equation can be written in slope intercept form y = m x +c where 'm' is the slope of the line, 'c' is the 'y-intercept'.
y = - (5.9/3.7) x + 2.1 [From equation (1)]
y = -(5.9/3.7) x + 2.1 [From equation (2)]
The both equation have same y-intercept. Therefore, the system of linear equations have infinitely many solution.
Hence, the system of linear equation -5.9x - 3.7y = -2.1 and 5.9x +3.7y = 2.1 have infinitely many solutions.
Learn more about the system of linear equation here
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