Math Problem Statement

y = 12 4x - y = 8

Solution

We have a system of equations to solve:

  1. y=12y = 12
  2. 4xy=84x - y = 8

Step 1: Substitute y=12y = 12 into the second equation.

Substitute yy into 4xy=84x - y = 8: 4x12=84x - 12 = 8

Step 2: Solve for xx.

Add 12 to both sides: 4x=204x = 20

Divide by 4: x=5x = 5

Final Answer:

x=5,y=12x = 5, \quad y = 12

Would you like more details about this process or additional examples?


Here are 5 related questions to explore:

  1. How do you solve systems of equations with substitution?
  2. Can you solve the same system using the elimination method?
  3. How would you solve the system if y=12y = 12 were instead y=4xy = 4x?
  4. What happens if the equations are parallel or identical?
  5. How do you graphically represent this solution?

Tip: Always substitute values back into the original equations to double-check your solutions!

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Math Problem Analysis

Mathematical Concepts

Algebra
Systems of Equations
Substitution Method

Formulas

y = 12
4x - y = 8

Theorems

Substitution method for solving systems of equations

Suitable Grade Level

Grades 7-9