Question

how many solutions does the system of equations below have?
3x + 9y = -4
3x - 19y = -2
no solution
one solution
infinitely many solutions
submit

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 \(3x + 9y=-4\), the slope \(m_1 = -\frac{3}{9}=-\frac{1}{3}\). For the second equation \(3x - 19y=-2\), the slope \(m_2 = -\frac{3}{-19}=\frac{3}{19}\). Since \(m_1
eq m_2\), the two lines are not parallel.

Step2: Determine the number of solutions

If two linear equations have different slopes, they are not parallel and will intersect at exactly one point. So the system of equations has one solution.

Answer:

one solution