Question

Solve each system by substitution.
1) y = 2x + 2
y = -5x + 16

Answer 1

y = 6

x = 2

Explanation:

rearrange the first equation in terms of x

x = (y - 2)/2

substiute x in the second equation

y = -5[(y-2)/2] +16

Now simpilify and solve for y

y = (-5y + 10)/2 +16

y = -5/2y + 5 + 16

y + 5/2y = 5 + 16

3.5y = 21

y = 6

Now substitue y in the first equation to solve for x

x = (6 - 2)/2

x = 2

Answer 2

(2, 6)

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

y = 2x + 2

y = -5x + 16

Step 2: Solve for x

Substitution

1. Substitute in y: 2x + 2 = -5x + 16
2. Add 5x on both sides: 7x + 2 = 16
3. Subtract 2 on both sides: 7x = 14
4. Divide 7 on both sides: x = 2

Step 3: Solve for y

1. Define equation: y = 2x + 2
2. Substitute in x: y = 2(2) + 2
3. Multiply: y = 4 + 2
4. Add: y = 6