-x + 2y = 21
5x + 6y = 23

(-5, 8)

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDASEquality Properties

Algebra I

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

Step-by-step explanation:

Step 1: Define systems

-x + 2y = 21

5x + 6y = 23

Step 2: Rewrite systems

-x + 2y = 21

Subtract 2y on both sides:                    -x = 21 - 2yDivide -1 on both sides:                         x = -21 + 2yRearrange:                                              x = 2y - 21

Step 3: Redefine systems

x = 2y - 21

5x + 6y = 23

Step 4: Solve for y

Substitution

Substitute in x:                         5(2y - 21) + 6y = 23Distribute 5:                             10y - 105 + 6y = 23Combine like terms:                16y - 105 = 23Add 105 on both sides:           16y = 128Divide 16 on both sides:          y = 8

Step 5: Solve for x

Define original equation:                    5x + 6y = 23Substitute in y:                                     5x + 6(8) = 23Multiply:                                                5x + 48 = 23Subtract 48 on both sides:                 5x = -25Divide 5 on both sides:                       x = -5

Step 6: Graph systems

Check the solution set.

( x , y ) = ( -5 , 8 )

The correct answer would be the fourth choice