Question

problem 3
graph two lines that match the description:
two lines with the same slope and same y - intercept.
how many solutions does this system of equations have?
no solution one solution infinitely many solutions

Explanation:

Step1: Recall line equation form

The slope - intercept form of a line is $y = mx + b$, where $m$ is the slope and $b$ is the $y$-intercept.

Step2: Analyze same slope and y - intercept

If two lines have the same slope ($m_1=m_2$) and the same $y$-intercept ($b_1 = b_2$), then their equations are identical ($y=m_1x + b_1$ and $y=m_2x + b_2$ with $m_1 = m_2$ and $b_1=b_2$).

Step3: Determine number of solutions

When two lines are identical, every point on one line is also on the other line. So, there are infinitely many points that satisfy both equations, which means there are infinitely many solutions.

Answer:

Infinitely many solutions