Question

how many solutions does the system of equations below have?
$y = -2x - \frac{7}{5}$
$y = \frac{2}{7}x + \frac{4}{9}$
no solution
one solution
infinitely many solutions
submit

Explanation:

Step1: Analyze the form of equations

Both equations are in slope - intercept form \(y = mx + b\), where \(m\) is the slope and \(b\) is the y - intercept. For the first equation \(y=-2x-\frac{7}{5}\), the slope \(m_1=-2\), and for the second equation \(y = \frac{2}{7}x+\frac{4}{9}\), the slope \(m_2=\frac{2}{7}\).

Step2: Compare the slopes

Since \(m_1=-2\) and \(m_2=\frac{2}{7}\), and \(m_1
eq m_2\). When two linear equations in two variables have different slopes, their graphs (which are straight lines) will intersect at exactly one point. So the system of equations has one solution.

Answer:

one solution