Math Problem Statement

Solve the puzzle involving the four equations: □ + □ = 4, □ + □ = 2, □ - □ = 5, □ = 7

Solution

Let's break down the math puzzle in the image and solve it step by step.

The puzzle consists of 4 equations involving boxes that we need to solve for:

  1. □ + □ = 4
  2. □ + □ = 2
  3. □ - □ = 5
  4. □ = 7

We'll solve this systematically by substituting and solving the unknowns.

From equation (4):

  • □ = 7 (this gives us one of the boxes as 7)

Now let's substitute the value 7 into the remaining equations.

For equation (3):

  • □ - 7 = 5
  • Solving for the other box:
    • □ = 5 + 7 = 12
  • So, the second box is 12.

Now, let's use these values in equation (2):

  • 7 + □ = 2
  • Solving for the missing box:
    • □ = 2 - 7 = -5
  • So, another box is -5.

Finally, for equation (1):

  • 12 + □ = 4
  • Solving for the last box:
    • □ = 4 - 12 = -8
  • So, the last box is -8.

Summary of the solution:

  • The four values are: 7, 12, -5, and -8.

Would you like further explanation on any of the steps or calculations?

Here are 5 follow-up questions to consider:

  1. What is the method used to solve a system of equations?
  2. How can substitution help solve for multiple variables?
  3. What happens when negative numbers are introduced into equations?
  4. How can we verify if all values satisfy the given puzzle?
  5. What are some other methods to solve puzzles with multiple unknowns?

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

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Math Problem Analysis

Mathematical Concepts

Basic Algebra
Linear Equations
Substitution

Formulas

Simple addition and subtraction

Theorems

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Suitable Grade Level

Grades 5-6