Solve the System of Equations -4x + 9y = 14 12x - 10y = - 8

(1, 2)

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to Right

Equality Properties

Multiplication Property of Equality Division Property of Equality Addition Property of Equality Subtract Property of Equality

Algebra I

Solving systems of equations using substitution/elimination

Step-by-step explanation:

Step 1: Define Systems

-4x + 9y = 14

12x - 10y = -8

Step 2: Rewrite Systems

-4x + 9y = 14

Multiply everything by 3:                    -12x + 27y = 42

Step 3: Redefine Systems

-12x + 27y = 42

12x - 10y = -8

Step 4: Solve for y

Elimination

Combine 2 equations:                    17y = 34Divide 26 on both sides:                y = 2

Step 5: Solve for x

Define equation:                    12x - 10y = -8Substitute in y:                       12x - 10(2) = -8Multiply:                                  12x - 20 = -8Isolate x term:                        12x = 12Isolate x:                                 x = 1

The answer would be 27 because assuming that each package has 1 bar of soap and 1 tube of toothpaste, after 27 packages they would run out of toothpaste