Math Problem Statement
Solution
The system of equations presented in the image is:
We are asked how many solutions this system has.
Step 1: Rewrite both equations in slope-intercept form
The first equation is already in slope-intercept form:
The second equation, , can be rewritten as:
Step 2: Compare the equations
We now have:
Both lines have the same slope () but different y-intercepts ( and ). Since they are parallel and have different y-intercepts, they never intersect.
Conclusion:
The system has 0 solutions because the lines are parallel and do not intersect.
Do you need more details or explanations?
Related Questions:
- What is the graphical meaning of parallel lines in a system of equations?
- How do we classify systems of equations by their number of solutions?
- What is the general approach to solving a system of linear equations?
- How can we use substitution to solve a system of equations?
- What are consistent, inconsistent, and dependent systems?
Tip:
When solving systems of linear equations, always check if the lines are parallel by comparing their slopes. Parallel lines mean no solutions.
Ask a new question for Free
By Image
Drop file here or Click Here to upload
Math Problem Analysis
Mathematical Concepts
Linear Equations
Slope-Intercept Form
Systems of Equations
Parallel Lines
Formulas
y = mx + b
Theorems
Parallel Line Theorem
Suitable Grade Level
Grades 8-10
Related Recommendation
Solve the System of Linear Equations x - y = 3 and 7x - y = -3 by Graphing
Graphing Linear Equations y = -x - 2 and y = x + 7 - Determine the Solution Count
Graphical Solution of the System of Linear Equations: x − y = 3 and 7x − y = −3
Solve and Analyze the System of Linear Equations: 7x - 3y = 3 and -21x + 9y = -5
Solve a System of Linear Equations by Graphing