Question

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

Answer 1

(5, -10)

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

Equality Properties

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

Algebra I

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

Explanation:

Step 1: Define Systems

-9x - 6y = 15

9x - 10y = 145

Step 2: Solve for y

Elimination

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

Step 3: Solve for x

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