Solving System of Equations: Find the Value of x

Math Problem Statement

The given system of equations has solution (x, y). What is the value of x?

To solve the given system of equations, we need to find the values of $x$ and $y$ . The system of equations is:

y = 3x \\ 4x - y = 14 \end{cases}$$ ### Step-by-Step Solution 1. **Substitute the expression for $$y$$ from the first equation into the second equation:** From the first equation, $$y = 3x$$. Substitute $$y = 3x$$ into the second equation: $$4x - (3x) = 14$$ 2. **Simplify the equation:** $$4x - 3x = 14$$ $$x = 14$$ 3. **Find the value of $$y$$ using the first equation:** Substitute $$x = 14$$ back into the equation $$y = 3x$$: $$y = 3(14)$$ $$y = 42$$ ### Conclusion The solution to the system of equations is $$x = 14$$ and $$y = 42$$. Thus, the value of $$x$$ is **14**. Would you like more details or have any questions? ### Related Questions: 1. How would the solution change if the second equation was $$4x + y = 14$$? 2. What are the graphical interpretations of these two linear equations? 3. How can we verify the solution algebraically? 4. How would you solve this system using matrix methods? 5. What happens if both equations are multiplied by a constant? Does the solution change? **Tip:** Always check your solutions by substituting them back into the original equations to ensure they satisfy both equations.

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Algebra
Systems of Linear Equations
Substitution Method

y = 3x
4x - y = 14

Linear Equations Solution Method

Grades 8-10

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