Math Problem Statement
11x–2y=5 4x+6y=9 What value of c will make this system have the same solution? 11x–2y=5 cx=24
Solution
To find the value of that will make the system:
have the same solution as the original system:
- ,
we need to express the second equation in terms of only , so we eliminate in both systems.
Step 1: Solve the second equation of the original system for
From the original system, the second equation is:
Solve for :
Step 2: Substitute this expression for in the first equation of the original system
Now substitute into the first equation :
Simplify: Multiply everything by 3 to eliminate the fraction:
Step 3: Substitute this value of into the equation
Now, from the second system, we know that . Substituting into this equation:
Multiply both sides by 37:
Thus, the value of that will make the system have the same solution is .
Would you like more details on any step?
Here are 5 related questions for further exploration:
- How can we verify that satisfies both systems?
- How would the solution change if the second equation had a different constant, such as ?
- How can you solve this system graphically?
- What happens if the value of is different from 37? Does the system still have a solution?
- Can you solve this system using substitution or elimination?
Tip: When solving systems of equations with different forms, always try to eliminate one variable first for clarity.
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Math Problem Analysis
Mathematical Concepts
Algebra
Systems of Linear Equations
Substitution Method
Formulas
Linear Equation: ax + by = c
Solving a system using substitution
Theorems
Consistency of a system of linear equations
Substitution Theorem
Suitable Grade Level
Grades 9-12
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