Question

Estimate the solution to the system of equations 7x−y=7 x+2y=6 ​i need help

Answer 1

(4/3, 7/3)

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 of using substitution/elimination

Explanation:

Step 1: Define Systems

7x - y = 7

x + 2y = 6

Step 2: Rewrite Systems

Equation: x + 2y = 6

1. [Subtraction Property of Equality] Subtract 2y on both sides: x = 6 - 2y

Step 3: Redefine Systems

7x - y = 7

x = 6 - 2y

Step 4: Solve for y

Substitution

1. Substitute in x: 7(6 - 2y) - y = 7
2. Distribute 7: 42 - 14y - y = 7
3. Combine like terms: 42 - 15y = 7
4. [Subtraction Property of Equality] Subtract 42 on both sides: -15y = -35
5. [Division Property of Equality] Divide -15 on both sides: y = 7/3

Step 5: Solve for x

1. Define original equation: x + 2y = 6
2. Substitute in y: x + 2(7/3) = 6
3. Multiply: x + 14/3 = 6
4. [Subtraction Property of Equality] Subtract 14/3 on both sides: x = 4/3