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3 years ago

4x - 2y = -20 7x + 2y = -2

Mathematics

1 answer:

Brut [27]3 years ago

8 0

Answer:

(-2, 6)

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS
Equality Properties

Algebra I

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

Step-by-step explanation:

Step 1: Define systems

4x - 2y = -20

7x + 2y = -2

Step 2: Rewrite systems

4x - 2y = -20

Add 2y to both sides: 4x = 2y - 20
Divide 4 on both sides: x = 1/2y - 5

Step 3: Redefine systems

x = 1/2y - 5

7x + 2y = -2

Step 4: Solve for y

Substitution

Substitute in x: 7(1/2y - 5) + 2y = =-2
Distribute 7: 7/2y - 35 + 2y = -2
Combine like terms: 11/2y - 35 = -2
Add 35 to both sides: 11/2y = 33
Isolate y: y = 6

Step 5: Solve for x

Define original equation: 7x + 2y = -2
Substitute in y: 7x + 2(6) = -2
Multiply: 7x + 12 = -2
Subtract 12 on both sides: 7x = -14
Divide 7 on both sides: x = -2

Step 6: Graph systems

Check the system.

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The sum of 1/6,2/3, and 1/4 is

Bumek [7]

¹³/₁₂

<h3>Further explanation</h3>

Given:

$\boxed{ \ \frac{1}{6} + \frac{2}{3} + \frac{1}{4} = ? \ }$

A fraction represents part of a whole.
A fraction consists of a numerator and a denominator. i.e., $\boxed{ \ \frac{numerator}{denominator} \ }$ .
The numerator = the number of equal parts of a whole.
The denominator = the total number of parts that make up said whole.

From the problems above, the denominator or the bottom numbers are still different. We use the Least Common Multiple (or LCM) to equalize the denominator.

Multiples of 3: $\boxed{ \ \{3, 6, 9, 12, 15, ... \} \ }$
Multiples of 4: $\boxed{ \ \{4, 8, 12, 16, ... \} \ }$
Multiples of 6: $\boxed{ \ \{6, 12, 18, ... \} \ }$

Hence, the LCM for 3, 4, and 6 is 12.

We change the denominator for each fraction to 12.

$\boxed{ \ \frac{1}{6} \rightarrow \frac{multiply \ by \ 2}{multiply \ by \ 2} \rightarrow \frac{2}{12} \ }$

$\boxed{ \ \frac{2}{3} \rightarrow \frac{multiply \ by \ 4}{multiply \ by \ 4} \rightarrow \frac{8}{12} \ }$

$\boxed{ \ \frac{1}{4} \rightarrow \frac{multiply \ by \ 3}{multiply \ by \ 3} \rightarrow \frac{3}{12} \ }$

Then we continue adding fractions.

$\boxed{ \ \frac{1}{6} + \frac{2}{3} + \frac{1}{4} = \frac{2}{12} + \frac{8}{12} + \frac{3}{12} \ }$

$\boxed{ \ \frac{1}{6} + \frac{2}{3} + \frac{1}{4} = \boxed{ \ \frac{13}{12} \ } \ }$

Thus, the result is $\boxed{ \ \frac{13}{12} \ or \ 1\frac{1}{12}\ }$

<h3>Learn more</h3>

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Keywords: the sum of ¹/₆, ²/₃, and ¹/₄, fraction, adding, numerator, denominator, still different, LCM

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