What is the solution of the system? y= 10x - 3 y= 7x + 2

(5/3, 41/3)

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 Subtraction Property of Equality

Algebra I

Terms/CoefficientsCoordinates (x, y)Solving systems of equations using substitution/eliminationSolving systems of equations by graphing

Step-by-step explanation:

Step 1: Define Systems

y = 10x - 3

y = 7x + 2

Step 2: Solve for x

Substitution

Substitute in y:                                                                                                 10x - 3 = 7x + 2[Subtraction Property of Equality] Subtract 7x on both sides:                           3x - 3 = 2[Addition Property of Equality] Add 3 on both sides:                                   3x = 5[Division Property of Equality] Divide 3 on both sides:                                x = 5/3

Step 3: Solve for y

Define original equation:                                                                                 y = 7x + 2Substitute in x:                                                                                                      y = 7(5/3) + 2Multiply:                                                                                                                y = 35/3 + 2Add:                                                                                                                     y = 41/3

Step 4: Check

Verify the solution set to the systems of equations by graphing the systems.

Where the 2 lines intersect is the solution set to the systems of equations.

We see graphically that point (1.666667, 13.66667), equivalent to (5/3, 41/3).

∴ (5/3, 41/3) or x = 5/3 and y = 41/3 is the solution to the systems of equations.