-x + 2y = 21 5x + 6y = 23
2 answers:
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
- Subtract 2y on both sides: -x = 21 - 2y
- Divide -1 on both sides: x = -21 + 2y
- 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>
- Substitute in <em>x</em>: 5(2y - 21) + 6y = 23
- Distribute 5: 10y - 105 + 6y = 23
- Combine like terms: 16y - 105 = 23
- Add 105 on both sides: 16y = 128
- Divide 16 on both sides: y = 8
<u>Step 5: Solve for </u><em><u>x</u></em>
- Define original equation: 5x + 6y = 23
- Substitute in <em>y</em>: 5x + 6(8) = 23
- Multiply: 5x + 48 = 23
- Subtract 48 on both sides: 5x = -25
- Divide 5 on both sides: x = -5
<u>Step 6: Graph systems</u>
<em>Check the solution set.</em>
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Step-by-step explanation:
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and
and