Solving a System of Linear Equations Using the Mixed Method

Math Problem Statement

Tolong selesaikan SPLDV ini dengan metode campuran

The system of linear equations (SPLDV) shown in the image is:

3x + y &= 7 \\ x + 4y &= 6 \end{align*}$$ You want to solve this using the mixed method, which typically involves a combination of substitution and elimination. ### Step 1: Solve one equation for one variable (Substitution method) Let's solve the second equation for $$x$$: $$x + 4y = 6 \quad \Rightarrow \quad x = 6 - 4y$$ ### Step 2: Substitute into the first equation Now, substitute $$x = 6 - 4y$$ into the first equation: $$3(6 - 4y) + y = 7$$ Expand and solve for $$y$$: $$18 - 12y + y = 7$$ $$18 - 11y = 7$$ $$-11y = 7 - 18$$ $$-11y = -11 \quad \Rightarrow \quad y = 1$$ ### Step 3: Substitute $$y = 1$$ back into the equation for $$x$$ Substitute $$y = 1$$ into $$x = 6 - 4y$$: $$x = 6 - 4(1)$$ $$x = 6 - 4 = 2$$ ### Final Solution: The solution to the system is: $$x = 2, \quad y = 1$$ Would you like further details or explanations? Here are some related questions: 1. How would the elimination method alone work for solving this system? 2. How do you verify if the solution $$x = 2$$ and $$y = 1$$ is correct? 3. Can this system of equations have more than one solution? 4. How do graphical methods compare to algebraic methods in solving systems like this? 5. How would the process change if the equations had fractions? **Tip:** Always double-check your solution by substituting the values of $$x$$ and $$y$$ back into both original equations to ensure they satisfy both.

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Algebra
Systems of Linear Equations

Substitution Method
Elimination Method

Basic Properties of Equality

Grades 8-10

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