Solving System of Equations Using Substitution Method

Math Problem Statement

Решите систему уравнений методом подстановки: 3x + 6y = -21, 3x - 12y = 51.

The task is to solve the following system of equations using the substitution method:

3x + 6y = -21, \\ 3x - 12y = 51. \end{cases}$$ Let's solve it step-by-step: ### Step 1: Solve one equation for one variable We'll start with the first equation: $$3x + 6y = -21.$$ We can solve for $$x$$: $$3x = -21 - 6y,$$ $$x = \frac{-21 - 6y}{3},$$ $$x = -7 - 2y.$$ ### Step 2: Substitute into the second equation Now substitute $$x = -7 - 2y$$ into the second equation $$3x - 12y = 51$$: $$3(-7 - 2y) - 12y = 51.$$ Simplify the equation: $$-21 - 6y - 12y = 51,$$ $$-21 - 18y = 51.$$ ### Step 3: Solve for $$y$$ Add 21 to both sides: $$-18y = 72.$$ Now divide by $$-18$$: $$y = -4.$$ ### Step 4: Solve for $$x$$ Now that we have $$y = -4$$, substitute this back into the equation $$x = -7 - 2y$$: $$x = -7 - 2(-4),$$ $$x = -7 + 8,$$ $$x = 1.$$ ### Final Answer: $$x = 1, \quad y = -4.$$ Would you like further clarification or have any questions? Here are some related questions: 1. How do you apply the substitution method to solve systems of equations? 2. What is the graphical interpretation of this solution? 3. How can you check the solution to a system of equations? 4. What is the elimination method for solving systems of linear equations? 5. How would you solve this system using matrices? **Tip:** Always double-check your solution by substituting the values of $$x$$ and $$y$$ back into the original equations.

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Linear Equations
Substitution Method

3x + 6y = -21
3x - 12y = 51

Substitution Method for Solving Systems of Equations

Grades 8-10

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