Math Problem Statement
Solution
The system of equations given in the image is:
You are tasked to solve this system graphically. To do so, you need to plot both lines on the provided graph and find their intersection point.
Steps to Solve:
-
Graph the first equation:
- Slope: (line decreases as increases).
- y-intercept: (the point ).
-
Graph the second equation:
- Slope: (line increases as increases).
- y-intercept: (the point ).
-
Plot both lines:
- For , plot the point and use the slope to go down 1 unit for every 2 units to the right.
- For , plot the point and use the slope to go up 3 units for every 2 units to the right.
-
Find the intersection:
- The lines intersect where their -values are equal, which solves the system of equations. Algebraically, you solve:
Solving for :
- Add to both sides:
- Add 5 to both sides:
- Divide by 2:
Solve for :
Substitute into either equation, e.g., :
Final Solution:
The intersection point is .
Do you need help plotting this solution on the graph or further clarification?
Here are 5 related questions for practice:
- What does the slope of a line tell you about its steepness and direction?
- Solve another system of equations: and .
- How do you determine the solution of a system graphically if the lines are parallel?
- What happens when two equations have the same line (identical)?
- Convert into slope-intercept form.
Tip: When solving graphically, ensure your graph is scaled correctly to make the intersection point clear!
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Math Problem Analysis
Mathematical Concepts
Linear Equations
Graphing Systems of Equations
Slope and Y-intercept
Formulas
Slope-intercept form: y = mx + b
Intersection of lines
Theorems
Two lines intersect where their y-values are equal.
Suitable Grade Level
Grades 8-10
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