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
To determine the solutions to the given system of linear equations by inspection, let's first compare the two equations.
Equation 1: y = -3x + 5
Equation 2: 2y = -6x + 10
By inspecting the second equation, we notice that the coefficients of x and y are the same as the first equation, but the right-hand side constant is multiplied by 2. This indicates that the two equations are multiples of each other, meaning they represent the same line.
In other words, the equations are parallel lines that will never intersect, which means there is no solution to the system of equations. Therefore, the correct answer is 2 (no solution).
By inspection, we can see that these two equations represent the same line. If we multiply the first equation by 2, we get:
2y = -6x + 10, which is the same as the second equation.
So, the system of linear equations has infinitely many solutions (3).
To solve the given system of linear equations by inspection, we can compare the coefficients of x and y in both equations.
First, let's rearrange the second equation to put it in slope-intercept form (y = mx + b), where m is the slope and b is the y-intercept:
2y = -6x + 10
Dividing both sides by 2:
y = -3x + 5
Now, we can see that the two equations are identical. This means that the system has infinitely many solutions.
Therefore, the answer is 3 (infinitely many solutions).