Question

how many solutions does the system of equations below have?
$y = 5x + 1$
$y = \frac{7}{6}x + \frac{3}{10}$
no solution
one solution
infinitely many solutions

Explanation:

Step1: Analyze the slopes

The equations are in slope - intercept form \(y = mx + b\), where \(m\) is the slope. For \(y = 5x+1\), the slope \(m_1 = 5\). For \(y=\frac{7}{6}x+\frac{3}{10}\), the slope \(m_2=\frac{7}{6}\). Since \(m_1
eq m_2\), the two lines are not parallel.

Step2: Determine the number of solutions

In a system of linear equations in two variables, if the two lines have different slopes (are not parallel and not coincident), they will intersect at exactly one point. So the system of equations has one solution.

Answer:

one solution