Question

how many solutions does the system of equations below have?
5x - 10y = 6
12x - 13y = -15
options: no solution, one solution, infinitely many solutions

Explanation:

Step1: Analyze the slopes of the lines

For a linear equation in the form \(ax + by = c\), the slope is \(-\frac{a}{b}\). For the first equation \(5x - 10y = 6\), the slope \(m_1=-\frac{5}{-10}=\frac{1}{2}\). For the second equation \(12x - 13y=- 15\), the slope \(m_2 =-\frac{12}{-13}=\frac{12}{13}\). Since \(m_1
eq m_2\), the two lines are not parallel and not coincident.

Step2: Determine the number of solutions

When two linear equations have different slopes, they intersect at exactly one point. So the system of equations has one solution.

Answer:

one solution