6. Solve the following pairs of simultaneous equations.
3x + y = 2
4x + 3y = 3

(3/5, 1/5)

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDASEquality Properties

Algebra I

Solving systems of equations using substitution/eliminationSolving systems of equations using graphing

Step-by-step explanation:

Step 1: Define systems

3x + y = 2

4x + 3y = 3

Step 2: Rewrite systems

y = 2 - 3x

4x + 3y = 3

Step 3: Solve for x

Substitute in y:                    4x + 3(2 - 3x) = 3Distribute 3:                         4x + 6 - 9x = 3Combine like terms:           -5x + 6 = 3Isolate x term:                     -5x = -3Isolate x:                              x = 3/5

Step 4: Solve for y

Define original equation:                  3x + y = 2Substitute in x:                                   3(3/5) + y = 2Multiply:                                              9/5 + y = 2Isolate y:                                             y = 1/5

Step 5: Check

Graph the systems of equations.

Step-by-step explanation:

STEP 1: Simplify

STEP 2: Multiply both sides of the equation by .

STEP 3: Remove parentheses.

STEP 4: Multiply

STEP 5: Move all terms not containing to the right side of the inequality.

STEP 6: Divide each term by and simplify.

STEP 7: The result can be shown in multiple forms.

Inequality Form:

Interval Notation:

,∞