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Arada [10]
2 years ago
7

Solve the system of equations {x−4y=3

Mathematics
2 answers:
lilavasa [31]2 years ago
8 0

Answer:

-1/3, 5/3

Step-by-step explanation:

Isolate x for x: -4y=3  x=3+4y

Substitute: x=3+4y

(2(3+4y)+y=3)

Isolate y for: 2(3+4y)+y=3    y=-1/3

Substitute: y=-1/3

3+4(-1/3)

3+4(-1/3)=5/3

x=5/3

-1/3,5/3


Arte-miy333 [17]2 years ago
5 0

Answer:

<h2>(-1, -1)</h2>

Step-by-step explanation:

Substitution\ method:\\\\\left\{\begin{array}{ccc}x-4y=3&\text{add 4y to both sides}\\2x+y=-3\end{array}\right\\\\\left\{\begin{array}{ccc}x=4y+3\\2x+y=-3\end{array}\right\\\\\text{Substitute from the first equation to the second equation:}\\\\2(4y+3)+y=-3\qquad\text{use distributive property}\\\\(2)(4y)+(2)(3)+y=-3\\\\8y+6+y=-3\qquad\text{subtract 6 from both sides}\\\\9y=-9\qquad\text{divide both sides by 9}\\\\\boxed{y=-1}\\\\\text{Put the value of y to the first equation:}\\\\x=4(-1)+3\\\\x=-4+3\\\\\boxed{x=-1}\\\\\boxed{\boxed{x=-1,\ y=-1\to(-1,\ -1)}}


Elimination\ method:\\\\\left\{\begin{array}{ccc}x-4y=3\\2x+y=-3&\text{multiply both sides by 4}\end{array}\right\\\underline{+\left\{\begin{array}{ccc}x-4y=3\\8x+4y=-12\end{array}\right}\qquad\text{add both sides of the equations}\\.\qquad\qquad9x=-9\qquad\text{divide both sides by 9}\\.\qquad\qquad\boxed{x=-1}\\\\\text{Put the value of x to the first equation:}\\\\-1-4y=3\qquad\text{add 1 to both sides}\\\\-4y=4\qquad\text{divide both sides by (-4)}\\\\\boxed{y=-1}\\\\\boxed{\boxed{x=-1,\ y=-1\to(-1,\ -1)}}

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Does the chart below represent a proportional relationship? What is the rate of change?
Lilit [14]

This chart represents a proportional relationship. The rate of change will be 4.

<h3>What is the constant of proportionality?</h3>

Firstly, there is a proportional relationship.

Two values x  and y are said to be in a proportional relationship if x=ky, where x and y are variables and k is a constant.

The constant k is called the constant of proportionality.

Given;

x y

1 4

2 8

3 12

4 16

Here, x = ky

put the first value

k = 1/4

This chart represents a proportional relationship.

So the rate of change will be

Rate = \dfrac{y_2 - y_1}{x_2 - x_1}\\\\Rate = \dfrac{8 - 4}{2 - 1}\\\\Rate = 4

Learn more about proportional ;

brainly.com/question/20048815

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5 0
2 years ago
Which of the following is the radical expression of a to the four ninths power ?
LuckyWell [14K]

Given expression in exponential form : a^{\frac{4}{9} }.

We need to convert it into radical form.

<em>Please note: When we convert an exponential to radical form, the top number goes in the exponent of the term and bottom number of the fraction goes in the radical sign to make it nth radical.</em>

We can apply following rule:

(a)^{\frac{m}{n}}= \sqrt[n]{x^m}.

Therefore,

a^{\frac{4}{9} }= \sqrt[9]{a^4}.

Therefore, correct option is : D. ninth root of a to the fourth power.

6 0
3 years ago
Can someone help with this please
Roman55 [17]
The scale is that 3 the force is going on a colicky of 350
8 0
2 years ago
Mitch used 1 4 pounds of beef to make 3 4 liters of beef strogonoff. If Mitch's recipe is for 1 liter of beef strogonoff, how ma
iren [92.7K]

option B) 3 pounds of beef is needed to make 6 times the recipe.

<u>Step-by-step explanation</u>:

<u>step 1 </u>:

Mitch used 14 pounds of beef = 34 liters of beef strogonoff

'x' pounds of beef = 1 liter of beef strogonoff

<u>step 2</u> :

Rate = No. of pounds / No. of liters

(14 pounds / 34 liters) = (x pounds / 1 liter)

x = 14/34

x = 0.412

1 liter of beef strogonoff = 0.412 pounds of beef

<u>step 3</u> :

To make 6 times the recipe = 6 \times 0.412

                                              = 2.5 pounds of beef ( approximately 3 pounds)

5 0
3 years ago
A trapezoid has a height of 6 inches, an area of 120 square inches, and one base measuring 13 inches. Find the length of the oth
kirill [66]

Answer:

27

Step-by-step explanation:

Givens

b1 = 13

b2 = ?

h = 6

Area = 120

Formula

Area = (b1 + b2) * h/2         Multiply by 2

2Area = (b1 + b2)*h           Divide by h

2Area/h = b1 + b2              Subtract b1 from both sides

2Area/h - b1 = b2

Solution

2*120 / 6 - 13 = b2

40 - 13 = b2

b2 = 27

It is always handy to solve an equation in the form that finds the unknown on one side. It makes the solution much easier.

6 0
3 years ago
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