Solve the system using linear combinations.
–5x + y = 1
9x – 2y = 4

(-6, -29)

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to Right

Equality Properties

Algebra I

Solving systems of equations using substitution/elimination

Step-by-step explanation:

Step 1: Define Systems

-5x + y = 1

9x - 2y = 4

Step 2: Rewrite Systems

-5x + y = 1

Add 5x on both sides:                    y = 5x + 1

Step 3: Redefine Systems

y = 5x + 1

9x - 2y = 4

Step 4: Solve for x

Substitution

Substitute in y:                    9x - 2(5x + 1) = 4Distribute -2:                       9x - 10x - 2 = 4Combine like terms:           -x - 2 = 4Isolate x term:                     -x = 6Isolate x:                              x = -6

Step 5: Solve for y

Define equation:                     -5x + y = 1Substitute in x:                         -5(-6) + y = 1Multiply:                                    30 + y = 1Isolate y:                                   y = -29

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