Question

how many solutions does the system of equations below have?
y = 7x - 2
y = 7x + \frac{1}{5}
no solution
one solution
infinitely many solutions
submit
work it out

Explanation:

Step1: Analyze the equations' slopes and y - intercepts

The two equations are in the slope - intercept form \(y = mx + b\), where \(m\) is the slope and \(b\) is the y - intercept.
For the equation \(y = 7x-2\), the slope \(m_1 = 7\) and the y - intercept \(b_1=-2\).
For the equation \(y = 7x+\frac{1}{5}\), the slope \(m_2 = 7\) and the y - intercept \(b_2=\frac{1}{5}\).

Step2: Determine the relationship between the lines

Since the slopes of the two lines are equal (\(m_1=m_2 = 7\)) and the y - intercepts are different (\(b_1
eq b_2\)), the two lines are parallel. Parallel lines in a plane do not intersect.

Answer:

no solution