Solving a System of Equations: x - 3y = 10 and 3x + y = 20

Math Problem Statement

Solve the system of equations: x - 3y = 10; 3x + y = 20

The system of equations given in the image is:

1. \quad x - 3y &= 10 \\ 2. \quad 3x + y &= 20 \end{aligned}$$ ### Solving the system using substitution or elimination: #### Step 1: Solve the first equation for $$x$$ From the first equation: $$x = 10 + 3y$$ #### Step 2: Substitute this expression for $$x$$ into the second equation: Substitute $$x = 10 + 3y$$ into the second equation $$3x + y = 20$$: $$3(10 + 3y) + y = 20$$ Simplifying: $$30 + 9y + y = 20 \\ 30 + 10y = 20$$ #### Step 3: Solve for $$y$$ $$10y = 20 - 30 \\ 10y = -10 \\ y = -1$$ #### Step 4: Substitute $$y = -1$$ back into the expression for $$x$$: $$x = 10 + 3(-1) = 10 - 3 = 7$$ ### Final Solution: $$x = 7, \quad y = -1$$ Would you like further details or clarifications? Here are some related questions: 1. How can we check if the solution is correct by substituting it back into the original system? 2. What are some other methods to solve systems of linear equations? 3. How does substitution compare to the elimination method? 4. What happens if we graph these equations? How does the solution appear visually? 5. Can a system of linear equations ever have no solution or infinite solutions? **Tip**: Always double-check your solution by substituting the values of the variables back into the original equations.

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Algebra
Systems of Linear Equations

Substitution Method
Elimination Method

Properties of Linear Equations

Grades 8-10

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