Solve the given system of linear equations by inspection. Enter 1 for one solution, 2 for no solution, or 3 for infinitely many solutions.
2x−7y=4
2x−7y=−4
2 for no solution
To determine if the system of linear equations has one solution, no solution, or infinitely many solutions, we need to compare the equations and coefficients.
Comparing the two equations, we can see that they have the same coefficients for both x and y variables. This means that the slope of the lines is the same.
If the lines have the same slope and different y-intercepts, then the system of equations has no solution.
However, if the lines have the same slope and the same y-intercept, then the system of equations has infinitely many solutions.
Let's compare the y-intercepts of the two equations:
For the first equation, when x = 0, we have:
2(0) - 7y = 4
-7y = 4
y = -4/7
For the second equation, when x = 0, we have:
2(0) - 7y = -4
-7y = -4
y = 4/7
Since the y-intercepts are different (-4/7 and 4/7), the system of linear equations has no solution.
Therefore, we enter 2 for no solution.
To solve the system of linear equations by inspection, we can observe the given equations and determine the relationship between them.
Looking at the given equations:
2x - 7y = 4 ...(Equation 1)
2x - 7y = -4 ...(Equation 2)
We can see that both equations have the same coefficients for x and y, which means they represent two parallel lines.
When two parallel lines have the same slope but different y-intercepts, they do not intersect and have no common point of intersection. Therefore, the system of equations has no solution (2).