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tensa zangetsu [6.8K]
3 years ago
9

Solve each system by elimination. 1) 6x - y=-14 -2x + y = 6

Mathematics
1 answer:
Verdich [7]3 years ago
7 0

Answer:

(-2, 2)

General Formulas and Concepts:

<u>Pre-Algebra</u>

Order of Operations: BPEMDAS

  1. Brackets
  2. Parenthesis
  3. Exponents
  4. Multiplication
  5. Division
  6. Addition
  7. Subtraction
  • Left to Right

Equality Properties

<u>Algebra I</u>

  • Solving systems of equations using substitution/elimination

Step-by-step explanation:

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

6x - y = -14

-2x + y = 6

<u>Step 2: Solve for </u><em><u>x</u></em>

<em>Elimination</em>

  1. Combine 2 equations:                    4x = -8
  2. Divide 4 on both sides:                   x = -2

<u>Step 3: Solve for </u><em><u>y</u></em>

  1. Define equation:                    -2x + y = 6
  2. Substitute in <em>x</em>:                       -2(-2) + y = 6
  3. Multiply:                                  4 + y = 6
  4. Isolate <em>y</em>:                                 y = 2
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The area of a rectangular wall of a barn is 85 square feet. Its length is 12 feet longer than the width. Find the length and wid
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Answer:

Length = 17 feet, Width = 5 feet

Step-by-step explanation:

Given:

The area of a rectangular wall of a barn is 85 square feet.

Its length is 12 feet longer than the width.

Question asked:

Find the length and width of the wall of the barn.

Solution:

Let width of a rectangular wall of a barn = x

<u>As length is 12 feet longer than the width.</u>

Length of a rectangular wall of a barn = 12+x

As we know:

Area\ of\ rectangle=length\times breadth

85=(12+x)x\\\\85=12x+x^{2} \\

Subtracting both sides by 85

x^{2} +12x-85=0\\x^{2} +17x-5x-85=0\\Taking\ common\\x+(x+17)-5x(x+17)=0\\(x+17)(x-5)=0\\x+17=0, x-5=0\\x=-17,x=5

As width can never be in negative, hence  width of a rectangular wall of a barn = x = 5 feet

Length of a rectangular wall of a barn = 12+x=12+5=17\ feet

Therefore, length and width of the wall of the barn is 17 feet and 5 feet respectively.

                 

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