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
The given system of linear equations is:
2x - 7y = 4
and
2x - 7y = -4
By inspection, we can see that the two equations are identical. This means that they represent the same line.
Therefore, the given system of linear equations has infinitely many solutions. So the answer is 3.
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Upon further inspection, we can see that the two equations have the same left-hand side, but different right-hand sides. Therefore, the equations do not represent the same line.
Since the coefficients of x and y are the same in both equations, we can subtract one equation from the other to eliminate x:
(2x - 7y) - (2x - 7y) = 4 - (-4)
0 = 8
This equation is not true, so there is no solution that satisfies both equations.
Therefore, the given system of linear equations has no solution. The answer is 2.
To solve this system of linear equations by inspection, we need to compare the two equations and determine if they represent the same line, parallel lines, or non-parallel lines.
Upon inspection, we can see that the coefficients of x and y in both equations are the same. The only difference is the constant term on the right-hand side of each equation.
Notice that if we multiply the second equation by -1, we would get:
-2x + 7y = 4
Now, we can observe that the two equations are identical. Both the coefficients and constant terms on both sides of the equation are the same.
Since the two equations represent the same line, they have infinitely many solutions.
Therefore, the answer is option 3 for infinitely many solutions.
To solve the given system of linear equations by inspection, we need to compare the coefficients of x and y in both equations.
First, let's compare the coefficients of x:
In the first equation, we have 2x.
In the second equation, we also have 2x.
Since the coefficients of x are the same in both equations, we move on to comparing the coefficients of y:
In the first equation, we have -7y.
In the second equation, we also have -7y.
Again, the coefficients of y are the same in both equations.
Now, let's compare the constants or the terms without any variable:
In the first equation, we have 4.
In the second equation, we have -4.
The constants are different in both equations.
Since the coefficients of x and y are the same, but the constants are different, we can conclude that there is no solution (Option 2) to this system of linear equations.
In summary, the system of linear equations has no solution.