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

(2, 1)

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets Parenthesis Exponents Multiplication Division Addition 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/CoefficientsSolving 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

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

Step 3: Solve for x

Substitution

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

Step 4: Solve for y

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

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