Math Problem Statement
y=-2x+8 y=-4x+16
Solution
Let's solve the system of linear equations:
Step 1: Set the equations equal to each other.
Since both equations equal , we set them equal:
Step 2: Solve for .
Simplify the equation:
Step 3: Solve for using .
Substitute into either equation (let's use the first one):
Solution:
The solution to the system is:
Verification:
Substitute into the second equation to ensure consistency: The solution is verified.
Would you like further details or have any questions about this process?
Here are 5 related questions to explore:
- How do you graphically interpret the solution to this system of equations?
- Can you identify if the system is consistent, inconsistent, or dependent?
- What happens if we modify one of the equations slightly (e.g., )?
- How would the solution differ if the two lines were parallel?
- Can we solve this system using matrices or another algebraic method?
Tip: Always verify solutions by substituting them back into the original equations!
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Math Problem Analysis
Mathematical Concepts
Algebra
Linear Equations
System of Equations
Formulas
Equation of a line: y = mx + b
Setting equations equal to solve for x and y
Theorems
Equality of two expressions for solving systems of equations
Suitable Grade Level
Grades 8-10
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