Question

does the system below have a unique solution, no solution, or many solutions? what does this mean graphically?
$2x + 7y = 10$
$x + 3.5y = 5$

does the system have a unique solution, no solution, or many solutions?
a. many solutions
b. no solution
c. a unique solution

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 $2x + 7y = 10$. This means the two equations represent the same line, so every point on the line is a solution.

Answer:

A. many solutions

Graphically, this means the two equations represent the exact same straight line, so there are infinitely many points (solutions) that lie on both lines.