Solve the given system of linear equations by inspection. y=35x−5 y=−35x−5 (1 point) Responses no solution no solution (0,−5) left parenthesis 0 comma negative 5 right parenthesis infinitely many solutions infinitely many solutions (−5,0)
The given system of linear equations is:
y = 35x - 5
y = -35x - 5
Since the two equations have the same y-intercept (-5), we can tell that they are parallel lines and do not intersect. Therefore, there is no solution. The correct response is "no solution".
To solve the system of linear equations by inspection, we need to observe the given equations and determine the relationship between their coefficients.
The coefficients for both equations are the same, except for the sign. This indicates that these equations are parallel lines. Parallel lines do not intersect, meaning there is no common solution. Therefore, the correct answer is "no solution".
To solve the given system of linear equations by inspection, we need to observe the relationship between the two equations and identify any patterns or clues that can help us find the solution.
Looking at the equations:
1. y = 35x - 5
2. y = -35x - 5
We can see that both equations have the same constant term "-5". This indicates that the lines represented by these equations are parallel, since they have the same y-intercept.
Furthermore, we observe that the coefficients of "x" in the two equations have opposite signs. In equation 1, it is positive (35x), and in equation 2, it is negative (-35x). This indicates that the slopes of the lines are opposite and equal in magnitude.
Given these observations, we can conclude that the two lines are parallel and will never intersect. Therefore, there is no common solution that satisfies both equations.
Hence, the correct response is "no solution."