Math Problem Statement
The graph of linear equation A passes through the points ( − 7 ,
4 ) and ( 3 , − 10 ) , while the graph of linear equation B passes through the points ( − 7 ,
4 ) and ( 5 ,
11 ) . Which of these is a solution to the system of equations consisting of linear equation A and linear equation B? A. ( − 7 ,
4 )
B. ( 3 , − 10 )
C. ( 5 ,
11 )
D. ( 7 ,
4 )
Solution
We are given two linear equations, A and B, that pass through the following points:
- Linear equation A: passes through points and
- Linear equation B: passes through points and
To find which point is a solution to the system of equations, we need to identify a point that is common to both lines. That is, the point must lie on both lines.
Step 1: Identify the common point between the two lines
The point appears in both sets of points for the two equations:
- Linear equation A passes through and .
- Linear equation B passes through and .
Thus, the point is the only point common to both lines.
Step 2: Verify the options
- Option A: is the common point for both equations.
- Option B: (3, -10) only lies on equation A, not equation B.
- Option C: (5, 11) only lies on equation B, not equation A.
- Option D: (7, 4) does not lie on either line.
Conclusion:
The solution to the system of equations is Option A: .
Would you like more details on how to derive the equations of these lines or any other clarification?
Here are some related questions you might find interesting:
- How do you find the equation of a line given two points?
- What is the slope-intercept form of a linear equation?
- How do you determine if two lines are parallel or perpendicular?
- How can you solve a system of linear equations graphically?
- What does the point of intersection represent in a system of equations?
Tip: When dealing with systems of linear equations, if two lines intersect at a single point, that point is the solution to the system.
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Math Problem Analysis
Mathematical Concepts
Linear Equations
Systems of Equations
Graphing Linear Equations
Formulas
Point-Slope Form of Linear Equation
Theorems
Intersection of Linear Equations
Suitable Grade Level
Grades 8-10
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