Question

does the system below have a unique solution, no solution, or
2x + 7y = 10
x + 3.5y = 5

does the system have a unique solution, no solution, or many sol
a. many solutions
b. no solution
c. a unique solution
what does this mean graphically?
a. the two lines are the same.
b. the two lines intersect at a single point.
c. the two lines are parallel.

Explanation:

Step1: Simplify the second equation

Multiply the second equation by 2:
$$2(x + 3.5y) = 2 \times 5$$
$$2x + 7y = 10$$

Step2: Compare the two equations

The simplified second equation is identical to the first equation $2x + 7y = 10$, meaning they represent the same line, which has infinitely many points (solutions).

Answer:

For the first question:
A. many solutions

For the second question:
A. The two lines are the same.