Question

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

Answer 1

Answer:

(-5, 8)

General Formulas and Concepts:

Pre-Algebra

• Order of Operations: BPEMDAS
• Equality Properties

Algebra I

• Solving systems of equations using substitution/elimination
• Solving 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

1. Subtract 2y on both sides:                    -x = 21 - 2y
2. Divide -1 on both sides:                         x = -21 + 2y
3. Rearrange:                                              x = 2y - 21

Step 3: Redefine systems

x = 2y - 21

5x + 6y = 23

Step 4: Solve for y

Substitution

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

Step 5: Solve for x

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

Step 6: Graph systems

Check the solution set.

Answer 2

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