Math Problem Statement

Solve the following system of equations. Write your answer as a point (π‘₯, 𝑦).

π‘₯ + 3𝑦 = 3 3π‘₯ + 𝑦 = 17

Solution

To solve the system of equations:

  1. x+3y=3x + 3y = 3
  2. 3x+y=173x + y = 17

Step 1: Solve one equation for one variable

From the first equation, solve for xx in terms of yy: x=3βˆ’3yx = 3 - 3y

Step 2: Substitute into the second equation

Substitute x=3βˆ’3yx = 3 - 3y into the second equation: 3(3βˆ’3y)+y=173(3 - 3y) + y = 17 Simplify: 9βˆ’9y+y=179 - 9y + y = 17 9βˆ’8y=179 - 8y = 17 βˆ’8y=8-8y = 8 y=βˆ’1y = -1

Step 3: Solve for xx

Substitute y=βˆ’1y = -1 back into x=3βˆ’3yx = 3 - 3y: x=3βˆ’3(βˆ’1)x = 3 - 3(-1) x=3+3x = 3 + 3 x=6x = 6

Final Answer:

The solution to the system is: (x,y)=(6,βˆ’1)(x, y) = (6, -1)

Would you like a detailed explanation or have any questions?


Related Questions:

  1. What are some alternative methods to solve systems of equations (e.g., elimination)?
  2. How can you verify that a solution to a system of equations is correct?
  3. Can this system of equations be solved graphically? How?
  4. What would the solution be if one of the equations were modified?
  5. How does solving systems of equations differ for non-linear systems?

Tip: Always double-check your solution by substituting the values back into the original equations.

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Math Problem Analysis

Mathematical Concepts

Algebra
Systems of Linear Equations
Substitution Method

Formulas

Substitution Method: Replace one variable with its equivalent from another equation
Simplification of linear equations

Theorems

Properties of Equality

Suitable Grade Level

Grades 8-10