Question

Solve the system.
y = 2x + 5
y=-3x

What is the solution?

Answer 1

x=−1 and y=3 or (-1,3)

WORK:

Let's solve your system by substitution.

y=2x+5;y=−3x

Step: Solve y=2x+5 for y:

y=2x+5

Step: Substitute 2x+5 for y in y=−3x:

y=−3x

2x+5=−3x

2x+5+3x=−3x+3x (Add 3x to both sides)

5x+5=0

5x+5+−5=0+−5(Add -5 to both sides)

5x ÷ 5 = -5÷5 (divide both sides with 5)

x=−1

Step: Substitute −1 for x in y=2x+5:

y=2x+5

y=(2)(−1)+5

y=3(Simplify both sides of the equation)

Answer:

x=−1 and y=3

(Incase you needed to show your work)

Hope this helps :)

Answer 2

(-1, 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
• Subtract Property of Equality

Algebra I

• Solving systems of equations using substitution/elimination

Explanation:

Step 1: Define Systems

y = 2x + 5

y = -3x

Step 2: Solve for x

Substitution

1. Substitute in y: -3x = 2x + 5
2. Add 3x on both sides: 0 = 5x + 5
3. Subtract 5 on both sides: -5 = 5x
4. Divide 5 on both sides: -1 = x
5. Rewrite: x = -1

Step 3: Solve for y

1. Define equation: y = -3x
2. Substitute in x: y = -3(-1)
3. Multiply: y = 3