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2 years ago

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

Mathematics

2 answers:

netineya [11]2 years ago

7 0

Answer:

(-5, 8)

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS
Equality Properties

Algebra I

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

Step-by-step explanation:

Step 1: Define systems

-x + 2y = 21

5x + 6y = 23

Step 2: Rewrite systems

-x + 2y = 21

Subtract 2y on both sides: -x = 21 - 2y
Divide -1 on both sides: x = -21 + 2y
Rearrange: x = 2y - 21

Step 3: Redefine systems

x = 2y - 21

5x + 6y = 23

Step 4: Solve for y

Substitution

Substitute in x: 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

Step 5: Solve for x

Define original equation: 5x + 6y = 23
Substitute in y: 5x + 6(8) = 23
Multiply: 5x + 48 = 23
Subtract 48 on both sides: 5x = -25
Divide 5 on both sides: x = -5

Step 6: Graph systems

Check the solution set.

9966 [12]2 years ago

6 0

( x , y ) = ( -5 , 8 )

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andrew11 [14]

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Step-by-step explanation:

The probability of Event B given Event A = the intersection of Event A and B divided by the probability of Event A. (see below for the symbols)

$P(B|A)=\dfrac{P(B\cap A)}{P(A)}$

P(A) = (1, 6), (1, 5), (1, 4), (1, 3), (1, 2), (1, 1)

(2, 6), (2, 5), (2, 4), (2, 3), (2, 2), (2, 1)

(3, 6), (3, 5), (3, 4), (3, 3), (3, 2), (3, 1)

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(5, 4), (5, 3), (5, 2), (5, 1)

(6, 3), (6, 2), (6, 1)

= 30

P(B) = (1, 2), (2, 1) sum = 3

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= 12

P(A ∩ B) = (1, 2), (2, 1)

(1, 5), (2, 4), (3, 3), (4, 2), (5, 1)

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3 years ago

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Svet_ta [14]

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---------------------

$8) \frac{10}{3x+1} =\frac{22}{7x-1}$

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$70x-10=66x+22$

$70x-66x=22+10$

$4x=32$

$x=\frac{32}{4}$

$x=8$

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hope it helps...

have a great day!!

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