Determine the number of solutions for the system by inspection and classify the system. 3x+7y=8 4x+y=10
A. The system has infinite solutions, so it is consistent and dependent.
B. The system has one solution, so it is consistent and dependent
C. The system has no solution, so it is inconsistent.
D. The system has one solution, so it is consistent and independent.
To determine the number of solutions for the system, we can start by checking if the two equations are independent or dependent.
We can rearrange the equations to be in slope-intercept form which is y = mx + b:
3x + 7y = 8
7y = -3x + 8
y = (-3/7)x + 8/7
4x + y = 10
y = -4x + 10
By inspection, we can see that the two equations have different slopes, so they are independent.
Since the two equations are independent, they intersect at one point, which means there is one solution.
Therefore, the answer is D. The system has one solution, so it is consistent and independent.