Question

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

Answer 1

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

Answer 2

(-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

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.