Math Problem Statement
3x+2y=45 4x -y=5
Solution
You've provided two linear equations:
This is a system of linear equations in two variables, and . We can solve this system using various methods, such as substitution, elimination, or matrix methods (like the determinant method). Let's use the substitution method here.
Step 1: Solve the second equation for
From the second equation:
Step 2: Substitute in the first equation
Now, substitute into the first equation: Simplify and solve for :
Step 3: Solve for
Now that we know , substitute it back into the expression for :
Solution
The solution to the system is:
This means the point is the intersection of the two lines represented by the equations.
Would you like to explore another method to solve this system or have any other questions?
Here are 5 related questions you might find interesting:
- What are the advantages of using the substitution method over the elimination method?
- How can you solve the system of equations using the elimination method?
- What does it mean if the system of equations has no solution or infinitely many solutions?
- How can you solve a system of linear equations using matrices?
- What is the graphical interpretation of the solution to a system of linear equations?
Tip: Always check your solution by substituting the values of and back into the original equations to verify they satisfy both equations.
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Math Problem Analysis
Mathematical Concepts
Linear Equations
Systems of Equations
Substitution Method
Formulas
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Theorems
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Suitable Grade Level
Grades 9-12
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