Solve the system of equations. −9x−6y=15 9x−10y=145

(5, -10)

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

BracketsParenthesisExponentsMultiplicationDivisionAdditionSubtractionLeft to Right  

Equality Properties

Multiplication Property of EqualityDivision Property of EqualityAddition Property of EqualitySubtraction Property of Equality

Algebra I

Terms/CoefficientsCoordinates (x, y)Solving systems of equations using substitution/eliminationSolving systems of equations by graphing

Step-by-step explanation:

Step 1: Define Systems

-9x - 6y = 15

9x - 10y = 145

Step 2: Solve for y

Elimination

Combine 2 equations:                                                                                   -16y = 160[Division Property of Equality] Divide -16 on both sides:                             y = -10

Step 3: Solve for x

Define original equation:                                                                                -9x - 6y = 15Substitute in y:                                                                                                -9x - 6(-10) = 15Multiply:                                                                                                           -9x + 60 = 15[Subtraction Property of Equality] Subtract 60 on both sides:                     -9x = -45[Division Property of Equality] Divide -9 on both sides:                               x = 5

Step 4: Check

Graph the systems of equations to verify the algebraically solved solution set is the solution.

Where the 2 lines intersect is the solution set.

We see graphically that we get (5, -10).

∴ (5, -10) or x = 5 and y = -10 is the solution to our systems