Question

unit: systems of equations
homework 3
name
date
pd
solving systems by graphing: part ii
complete the following sentences with “the same” or “different” in order to make the sentence a true statement.

1. when graphing a system of equations with no solution, the slopes of the two lines will be .
2. when graphing a system of equations with infinitely many solutions, the slopes of the two lines will be .
3. when graphing a system of equations with no solution, the y - intercept of the two lines will be .
4. when graphing a system of equations with infinitely many solutions, the y - intercept of the two lines will be .
5. when graphing a system of equations with one solution, the slopes of the two lines will be .

Explanation:

Step1: Recall system of equations graphing rules

For a system of linear equations in the form \(y = mx + b\) (where \(m\) is slope and \(b\) is y - intercept):

• No solution (parallel lines): Parallel lines have the same slope (\(m_1=m_2\)) and different y - intercepts (\(b_1

eq b_2\)).

• Infinitely many solutions (coincident lines): Coincident lines have the same slope (\(m_1 = m_2\)) and the same y - intercept (\(b_1=b_2\)).
• One solution (intersecting lines): Intersecting lines have different slopes (\(m_1

eq m_2\)).

Step2: Answer each question

1. When graphing a system of equations with no solution (parallel lines), the slopes of the two lines will be the same.
2. When graphing a system of equations with infinitely many solutions (coincident lines), the slopes of the two lines will be the same.
3. When graphing a system of equations with no solution (parallel lines), the y - intercept of the two lines will be different.
4. When graphing a system of equations with infinitely many solutions (coincident lines), the y - intercept of the two lines will be the same.
5. When graphing a system of equations with one solution (intersecting lines), the slopes of the two lines will be different.

Answer:

1. the same
2. the same
3. different
4. the same
5. different