Question

how many solutions does the system of equations below have?
y = -x - 4
y = \frac{-5}{8}x + \frac{7}{8}
no solution
one solution
infinitely many solutions
submit

Explanation:

Step1: Analyze the slopes of the two lines

The first equation \( y = -x - 4 \) is in slope - intercept form \( y=mx + b \), where the slope \( m_1=- 1\). The second equation \( y=\frac{-5}{8}x+\frac{7}{8} \) is also in slope - intercept form, and its slope \( m_2 =-\frac{5}{8}\). Since \( m_1
eq m_2 \), the two lines are not parallel.

Step2: Determine the number of solutions

For a system of linear equations in two variables (in the form \( y = m_1x + b_1\) and \( y=m_2x + b_2\)), if the slopes are different (\( m_1
eq m_2\)), the two lines intersect at exactly one point. So the system of equations has one solution.

Answer:

one solution