How many solutions does the system of equations have? 8x−6y=48 8x+6y=48(1 point) Responses two two none none one one infinite
The correct response is one. The given system of equations is consistent and independent, as the equations are not identical and their coefficients are not proportional to each other. Therefore, there is a unique solution to the system.
To determine how many solutions a system of equations has, we can compare the coefficients of the variables in the equations. In this case, let's examine the coefficients of the variable x.
First equation: 8x - 6y = 48
Second equation: 8x + 6y = 48
The coefficients of x in both equations are the same, which means the lines represented by these equations are parallel. When parallel lines are considered, there are no solutions.
Therefore, the answer is none.
To determine the number of solutions for the given system of equations, we need to analyze the equations and their relationship.
Let's start by simplifying the two equations:
Equation 1: 8x - 6y = 48
Equation 2: 8x + 6y = 48
Now, let's do a comparison between the two equations. Notice that the coefficients of the variables 'y' in both equations are the same (6 and -6), but with different signs.
When the coefficients of the variables in a system of equations have different signs, it indicates that the lines represented by the equations are parallel. In this case, both lines have the same slope, but the y-intercepts differ because of the opposite signs.
Since parallel lines never intersect, the system of equations has NO solutions. Therefore, the correct answer is "none".