Question

how many solutions does the system of equations below have?
y = 10x + 6
y = \frac{9}{8}x + \frac{5}{4}
no solution
one solution
infinitely many solutions
submit

Explanation:

Step1: Analyze the slopes

The equations are in slope - intercept form \(y = mx + b\), where \(m\) is the slope and \(b\) is the y - intercept. For the first equation \(y=10x + 6\), the slope \(m_1=10\). For the second equation \(y=\frac{9}{8}x+\frac{5}{4}\), the slope \(m_2 = \frac{9}{8}\).

Step2: Compare slopes and y - intercepts

Since \(m_1=10
eq m_2=\frac{9}{8}\), the two lines are not parallel. Also, since the slopes are different, the two lines will intersect at exactly one point. When two lines in a system of linear equations have different slopes, the system has one solution.

Answer:

one solution