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

(3, 0)

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets Parenthesis Exponents Multiplication Division Addition 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/eliminationSolving systems of equations by graphingTerms/Coefficients

Step-by-step explanation:

Step 1: Define Systems

3x - y = 9

2x - y = 6

Step 2: Rewrite Systems

2x - y = 6

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

Step 3: Redefine Systems

3x - y = 9

y = 2x - 6

Step 4: Solve for x

Substitution

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

Step 5: Solve for y

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

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