Question

Which ordered pair is the solution to the system of linear equations -5x + Y = 26 and 2x-7y = 16 ?

Answer 1

(-6, -4)

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
• Subtract Property of Equality

Algebra I

• Terms/Coefficients
• Solving systems of equations using substitution/elimination

Explanation:

Step 1: Define Systems

-5x + y = 26

2x - 7y = 16

Step 2: Rewrite Systems

-5x + y = 26

1. Add 5x on both sides: y = 5x + 26

Step 3: Redefine Systems

y = 5x + 26

2x - 7y = 16

Step 4: Solve for x

Substitution

1. Substitute in y: 2x - 7(5x + 26) = 16
2. Distribute -7: 2x - 35x - 182 = 16
3. Combine like terms: -33x - 182 = 16
4. Isolate x term: -33x = 198
5. Isolate x: x = -6

Step 5: Solve for y

1. Define equation: 2x - 7y = 16
2. Substitute in x: 2(-6) - 7y = 16
3. Multiply: -12 - 7y = 16
4. Isolate y term: -7y = 28
5. Isolate y: y = -4