Question

Select the correct answer.

What is the difference of the values of the two variables in this system of equations?
y=2x+1
x+3y= 10
OA. 0
OB. 1
Ос.
2
OD. 3

Answer 1

C. 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

Equality Properties

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

Algebra I

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

Explanation:

Step 1: Define Systems

y = 2x + 1

x + 3y = 10

Step 2: Solve for x

Substitution

1. Substitute in y: x + 3(2x + 1) = 10
2. Distribute 3: x + 6x + 3 = 10
3. Combine like terms: 7x + 3 = 10
4. [Subtraction Property of Equality] Subtract 3 on both sides: 7x = 7
5. [Division Property of Equality] Divide 7 on both sides: x = 1

Step 3: Solve for y

1. Define original equation: y = 2x + 1
2. Substitute in x: y = 2(1) + 1
3. Multiply: y = 2 + 1
4. Add: y = 3

Step 4: Find difference

y = 3

x = 1

1. Subtract: 3 - 1 = 2