Solve the given system of linear equations by inspection. Enter 1 for one solution, 2 for no solution, or 3 for infinitely many solutions.
y=−3x+5
2y=−6x+10
(1 point)
The given system of linear equations is:
y = -3x + 5
2y = -6x + 10
From inspection, we can see that these two equations represent the same line. The second equation is simply obtained by multiplying the first equation by 2 on both sides.
Since the equations represent the same line, they have infinitely many solutions.
Therefore, the answer is 3 for infinitely many solutions.
To solve the given system of linear equations by inspection, we need to compare the equations and check if they represent the same line or parallel lines.
Looking at the two equations:
1) y = -3x + 5
2) 2y = -6x + 10
We can see that equation 2) is simply equation 1) multiplied by 2.
Therefore, the two equations represent the same line.
Since the equations represent the same line, there are infinitely many solutions.
Hence, the answer is 3 (infinitely many solutions).
To solve the given system of linear equations by inspection, we need to compare the two equations and determine their relationship.
By inspecting the equations, we can see that they are parallel lines. This means they have the same slope (-3 in both equations) and different y-intercepts (5 and 10 in the two equations).
When two lines are parallel, they will never intersect, meaning there is no common solution. Therefore, the system of equations has no solution.
Hence, the answer is 2 (no solution).