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netineya [11]
2 years ago
5

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

Mathematics
2 answers:
netineya [11]2 years ago
7 0

Answer:

(-5, 8)

General Formulas and Concepts:

<u>Pre-Algebra</u>

  • Order of Operations: BPEMDAS
  • Equality Properties

<u>Algebra I</u>

  • Solving systems of equations using substitution/elimination
  • Solving systems of equation by graphing

Step-by-step explanation:

<u>Step 1: Define systems</u>

-x + 2y = 21

5x + 6y = 23

<u>Step 2: Rewrite systems</u>

-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

<u>Step 3: Redefine systems</u>

x = 2y - 21

5x + 6y = 23

<u>Step 4: Solve for </u><em><u>y</u></em>

<em>Substitution</em>

  1. Substitute in <em>x</em>:                         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

<u>Step 5: Solve for </u><em><u>x</u></em>

  1. Define original equation:                    5x + 6y = 23
  2. Substitute in <em>y</em>:                                     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

<u>Step 6: Graph systems</u>

<em>Check the solution set.</em>

9966 [12]2 years ago
6 0
( x , y ) = ( -5 , 8 )
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