Question

graph these equations:
$y = -\frac{3}{5}x + 4$
$y = -\frac{3}{5}x + 8$
click to select points on the graph.
how many solutions does the system of equations have?
no solution
one solution
infinitely many solutions

Explanation:

Step1: Analyze the slopes and y-intercepts

The two equations are in slope - intercept form \(y = mx + b\), where \(m\) is the slope and \(b\) is the y - intercept. For the equation \(y=-\frac{3}{5}x + 4\), the slope \(m_1=-\frac{3}{5}\) and the y - intercept \(b_1 = 4\). For the equation \(y=-\frac{3}{5}x+8\), the slope \(m_2 = -\frac{3}{5}\) and the y - intercept \(b_2=8\). Since \(m_1=m_2\) (the slopes are equal) and \(b_1
eq b_2\) (the y - intercepts are different), the two lines are parallel.

Step2: Determine the number of solutions

Parallel lines never intersect. In a system of linear equations, the solution is the point of intersection of the two lines. If two lines are parallel and do not intersect, the system of equations has no solution.

Answer:

no solution