Solve the System of Equations x - 3y = 2 and 5x + y = -54 using Substitution

Math Problem Statement

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Solve the following system of equations with the substitution method: { x - 3y = 2, 5x + y = -54 }

We are given the following system of equations:

x - 3y = 2 \\ 5x + y = -54 \end{cases}$$ To solve this using the substitution method, follow these steps: ### Step 1: Solve one equation for one variable We can start by solving the first equation $$x - 3y = 2$$ for $$x$$: $$x = 3y + 2$$ ### Step 2: Substitute this expression for $$x$$ into the second equation Substitute $$x = 3y + 2$$ into the second equation $$5x + y = -54$$: $$5(3y + 2) + y = -54$$ ### Step 3: Solve for $$y$$ Now, expand and simplify the equation: $$15y + 10 + y = -54$$ $$16y + 10 = -54$$ $$16y = -64$$ $$y = -4$$ ### Step 4: Substitute $$y = -4$$ back into the expression for $$x$$ Substitute $$y = -4$$ into $$x = 3y + 2$$: $$x = 3(-4) + 2 = -12 + 2 = -10$$ ### Final Answer: The solution to the system is $$(x, y) = (-10, -4)$$. Let me know if you would like further details or explanations! Here are 5 related questions you might find interesting: 1. How would the solution process change if we used elimination instead of substitution? 2. Can you confirm the solution by plugging $$x = -10$$ and $$y = -4$$ back into the original equations? 3. What is the geometric interpretation of solving systems of linear equations? 4. How can substitution be used for non-linear systems of equations? 5. How do you handle systems of equations with more than two variables? **Tip:** Always double-check your solution by substituting the values of the variables back into both original equations to ensure they satisfy the system.

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Algebra
Systems of Equations
Substitution Method

Substitution method
Linear equations

Grades 8-10

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