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Marina86 [1]
3 years ago
10

4y-x=5+2y; 3x+7y=24 solve systen by using substitution

Mathematics
1 answer:
jek_recluse [69]3 years ago
6 0
4y - x = 5 + 2y ..... (1)
3x + 7y = 24    ..... (2)

by grouping like terms in (1)
4y - x = 5 + 2y
4y - 2y - x = 5
<span>-x + 2y = 5 </span>        ..... (1a)

by multiplying (1a) through by -3
(-3)(-x) + 2(-3)y = 5(-3)
3x  -  6y = -15  ..... (1b)

by subtracting 1a from 2
3x -3x + 7y - (-6y) = 24 - (-15)
                      13y = 39
           ⇒            y = 3

by substituting y=3 into (2)
    3x + 7(3) = 24 
              3x = 24 - 21
              3x = 3
        ⇒     x = 1


∴ solution to the system is x=1 when y = 3
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Answer:

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Step-by-step explanation:

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3 years ago
Let f(x) = 4x – 2 and g(x) = x + 1. Find the following function value.<br> (f - g)(-3)
Nataly [62]

Answer:

(f - g)(3) = 6

General Formulas and Concepts:

<u>Pre-Algebra</u>

  • Order of Operations: BPEMDAS

<u>Algebra I</u>

  • Function Notation

Step-by-step explanation:

<u>Step 1: Define</u>

f(x) = 4x - 2

g(x) = x + 1

<u>Step 2: Find</u>

<em>Find (f - g)(x)</em>

  1. Substitute:                         (f - g)(x) = 4x - 2 - (x + 1)
  2. Distribute -1:                      (f - g)(x) = 4x - 2 - x - 1
  3. Combine like terms:         (f - g)(x) = 3x - 3

<em>Find (f - g)(3)</em>

  1. Substitute:                         (f - g)(3) = 3(3) - 3
  2. Multiply:                             (f - g)(3) = 9 - 3
  3. Subtract:                            (f - g)(3) = 6
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Alexandra [31]
I: y<2*x
II: y<8
III: x>2

a: (5,3):
I: 3<2*5
3<10 ?yes
II: 3<8 ?yes
III: 5>2 ?yes
This is a solution

b: (6,0):
I: 0<2*6
0<12 ?yes
II: 0<8 ?yes
III: 6>2 ?yes
This is a solution

c: (3,3):
I: 3<2*3
3<6 ?yes
II: 3<8 ?yes
III: 3>2 ?yes
This is a solution

d: (1,-4):
I: -4<2*1
-4<2 ?yes
II: -4<8 ?yes
III: 1>2 ?no
This is not a solution

e: (4,-2):
I: -2<2*4
-2<8 ?yes
II: -2<8 ?yes
III: 4>2 ?yes
This is a solution

f: (5,9):
I: 9<2*5
9<10 ?yes
II: 9<8 ?no
This is not a solution

so a,b,c,e are solutions and d,f not
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The weight of 10,000 identical samples of a substance is 10 pounds. What is the weight of 10 samples?
boyakko [2]

0.01 pounds is the answer

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3 years ago
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