Question

Solve each system of eaquasions x+4y=4 -x+2y=8​

Answer 1

x + 4y = 4
-x + 2y = 8


x + 4y - x + 2y = 4 + 8

6y = 12

y = 2


x + 4(2) = 4
x + 8 = 4
x = -4

(x,y)
(-4,2)

Answer 2

(-4, 2)

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

Distributive Property

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 systems

Explanation:

Step 1: Define Systems

x + 4y = 4

-x + 2y = 8

Step 2: Rewrite Systems

x + 4y = 4

1. [Subtraction Property of Equality] Subtract 4y on both sides: x = 4 - 4y

Step 3: Redefine Systems

x = 4 - 4y

-x + 2y = 8

Step 4: Solve for y

Substitution

1. Substitute in x: -(4 - 4y) + 2y = 8
2. [Distributive Property] Distribute negative: -4 + 4y + 2y = 8
3. Combine like terms: -4 + 6y = 8
4. [Addition Property of Equality] Add 4 on both sides: 6y = 12
5. [Division Property of Equality] Divide 6 on both sides: y = 2

Step 5: Solve for x

1. Define original equation: x + 4y = 4
2. Substitute in y: x + 4(2) = 4
3. Multiply: x + 8 = 4
4. [Subtraction Property of Equality] Subtract 8 on both sides: x = -4