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Gnom [1K]
2 years ago
9

Solve the given system by substitution.

Mathematics
2 answers:
denis-greek [22]2 years ago
8 0

Answer:

Step-by-step explanation:

5m = 2/3m - 13

15m = 2m - 39

13m = -39

m = -3

n = 5(-3)

n = -15

(-3, -15)

alekssr [168]2 years ago
4 0

Answer:

(-3, -15)

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>

n = 5m

n = 2/3m - 13

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

<em>Substitution</em>

  1. Substitute in <em>n</em>:                                 5m = 2/3m - 13
  2. Subtract 2/3m on both sides:          13/3m = -13
  3. Divide 11/3 on both sides:                m = -3

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

  1. Define equation:                    n = 5m
  2. Substitute in <em>m</em>:                      n = 5(-3)
  3. Multiply:                                  n = -15
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Your problem statement makes no reference to p or q, so we can only guess that "p/q" refers to the ratio of the lowest- and highest-degree coefficients:

... -6/1

Then the factors of p/q are the factors of 6, with either sign.

Factors of p/q: ±1, ±2, ±3.

There are a number of ways the factors can be tested. To test 1, simply add the coefficients. (The sum is -8.) To test -1, subtract the sum of odd-degree coefficients from the sum of even-degree coefficients. (The difference is 0.)

Knowing that -1 is a root of the function, you can use synthetic division to find the quadratic factor. (See the first attachment for the work.) Then you have ...

... f(x) = (x +1)(x² +x -6)

You can continue to test the factors of p/q, or you can factor the quadratic to get ...

... f(x) = (x +1)(x -2)(x +3)

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Y-intercept: -6

As with any odd-degree polynomial with a positive leading coefficient, the overall behavior looks like "/". That is ...

End behaviors: f(x) goes to -∞ as x goes to -∞; f(x) goes to +∞ as x goes to +∞.

_____

A graph of f(x) is shown in the third attachment. (Graphing calculators make it easy to use graphing to find x-intercepts.)

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