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What is the solution to the pair of simultaneous equations? 2x+y=5. 3x-2y=4​

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Answer:

(2, 1)

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

  1. Brackets
  2. Parenthesis
  3. Exponents
  4. Multiplication
  5. Division
  6. Addition
  7. Subtraction
  • Left to Right  

Distributive Property

Equality Properties

  • Multiplication Property of Equality
  • Division Property of Equality
  • Addition Property of Equality
  • Subtraction Property of Equality

Algebra I

  • Coordinates (x, y)
  • Terms/Coefficients
  • Solving systems of equations using substitution/elimination

Step-by-step explanation:

Step 1: Define Systems

2x + y = 5

3x - 2y = 4

Step 2: Rewrite Systems

Manipulate 1st equation

  1. [Subtraction Property of Equality] Subtract 2x on both sides:                      y = 5 - 2x

Step 3: Solve for x

Substitution

  1. Substitute in y [2nd Equation]:                                                                         3x - 2(5 - 2x) = 4
  2. [Distributive Property] Distribute -2:                                                                3x - 10 + 4x = 4
  3. [Addition] Combine like terms:                                                                        7x - 10 = 4
  4. [Addition Property of Equality] Add 10 on both sides:                                   7x = 14
  5. [Division Property of Equality] Divide 7 on both sides:                                 x = 2

Step 4: Solve for y

  1. Substitute in x [Modified 1st Equation]:                                                           y = 5 - 2(2)
  2. Multiply:                                                                                                             y = 5 - 4
  3. Subtract:                                                                                                            y = 1
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