Question

Determine the solution to the system of equations. 3x - y = 9 2x - y = 6

Answer 1

Answer:

(3, 0)

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
• Solving systems of equations by graphing
• Terms/Coefficients

Step-by-step explanation:

Step 1: Define Systems

3x - y = 9

2x - y = 6

Step 2: Rewrite Systems

2x - y = 6

1. Subtract 2x on both sides:                    -y = 6 - 2x
2. Divide -1 on both sides:                         y = 2x - 6

Step 3: Redefine Systems

3x - y = 9

y = 2x - 6

Step 4: Solve for x

Substitution

1. Substitute in y:                         3x - (2x - 6) = 9
2. Distribute -1:                             3x - 2x + 6 = 9
3. Combine like terms:                x + 6 = 9
4. Isolate x:                                   x = 3

Step 5: Solve for y

1. Define equation:                     2x - y = 6
2. Substitute in x:                        2(3) - y = 6
3. Multiply:                                   6 - y = 6
4. Isolate y term:                         -y = 0
5. Isolate y:                                  y = 0

Step 6: Check

Graph the systems to verify the solution set (3, 0) is the solution.

The solution set to the systems would be where the 2 lines intersect.

We see that the intersection point is x-intercept (3, 0).

∴ (3, 0) is the solution set to the systems of equations.

Answer 2

isolate and solve for y

Step-by-step explanation:

subtract y from both sides than divide the x values from bothe sides