solve the simultaneous equations
5x + 6y = 3
2x - 3y = 12

Answers

Answer 1

Answer: x =3; y = -2

[tex]\left \{ {{5x+6y=3} \atop {2x-3y=12}} \right.\\\\<=>\left \{ {{x=\frac{3-6y}{5} } \atop {2x-3y=12}} \right.\\\\<=>\left \{ {{x=\frac{3-6y}{5} } \atop {2.\frac{3-6y}{5}-3y =12}} \right.\\\\<=>\left \{ {{x=\frac{3-6y}{5} } \atop {6-12y-15y=12.5}} \right.\\\\<=>\left \{ {{x=\frac{3-6y}{5} } \atop {17y=6-60=-54}} \right.\\\\<=>\left \{ {{x=\frac{3-6y}{5} } \atop {y=-54/27}} \right.\\\\\\ <=>\left \{ {{x=\frac{3-6y}{5} } \atop {y=-2}} \right.\\\\<=>\left \{ {{x=3} \atop {y=-2}} \right.[/tex]

Step-by-step explanation:

Answer 2

Answer:

x = 3, y = -2.

Step-by-step explanation:

5x + 6y = 3

2x - 3y = 12           Multiply this by 2:

4x - 6y = 24           Now add this to the first equation:

9x = 27

x = 3.

Substitute x = 3 in the second equation:

2(3) - 3y = 12

-3y = 12 - 6 = 6

y = 6 / -3

y = -2.


Related Questions

The difference between two numbers is 8. Twice the number is 4 more than the larger number. What is the smaller number?

Answers

Answer:

If the two numbers are x and y, then:

x + y = 8

18 - 2x = 4y - 2.

When we subtract y from both sides in our first equation we get:

x = 8 - y, so:

18 - 2(8 - y) = 4y - 2

18 - 16 + 2y = 4y - 2

2 + 2y = 4y - 2

2y = 4

y = 2

Since x + y = 8, and y = 2, x = 6, and since 6 > 2, the larger number is 6.

Is it possible to solve 1+1 in a algebraic form?

Answers

Answer:

i dont think so but 1+1=

baby 1 see theirs a daddy 1 and a mommy 1 so that =baby 1

Step-by-step explanation:

solve and graph this equation. x - 1 <2x + 3 < x + 4?

Answers

Answer:

Answer = (-4,1)

Step-by-step explanation:

Janice wanted to calculate 3/5 of the sale price of new jeans on her calculator. Which decimal should she type into her calculator that has the same value as 3/5?

Answers

The answer is 0.6. I hope this helps

Explain what needs to be fixed.
2n + 10 = -2
2n = 12 Step one
n = 6 Step two

Answers

Answer:

step one needs to be fixed... you are supposed to subtract 10 from both sides of the equation.

Step-by-step explanation:

STEP 1: Move all terms not containing n to the right side of the equation.

[tex]2n=-12[/tex]

STEP 2: Divide each term by 2 and simplify.

[tex]n=-6[/tex]

Plzzzzzzz helppppppp

Answers

Answer:

a i think

Step-by-step explanation:

Answer:

Y = -5 + 5

Step-by-step explanation:

You can check the y intercept and it's a negative 5 slope

5. Past experience shows that the standard deviation of the distances traveled by consumers to patronize Chinese restaurants is 2 km. How large a sample is needed to estimate the population mean distance traveled to within 0.4 km

Answers

Answer:

96

Step-by-step explanation:

Given that :

Standard deviation (s) = 2km

Error in estimation is within 0.4 km ; Error (E) = 0.4 km

Using the relation :

Sample size = ((Zα/2 * s) /E)^2

Using α = 0.05

The Zcritical at 0.05 = Z0.025 = 1.96

Sample size = ((1.96 * 2) / 0.4)^2

Sample size = (3.92 / 0.4)^2

Sample size = 9.8²

Sample size = 96.04

Required sample size = 96

d=1/2at^2+s, solve for a

Answers

Step-by-step explanation:

Perhaps the equation is d=1/2at2 and you are given the distance (40 m) and acceleration (9.8 m/s2) and asked to find the time. or convert the equation in terms of t and then plug in the numbers to solve.

A line has a slope of 9 and passes through the point (4, 5). What is its equation in point-slope form?​

Answers

Answer:

y - 5 = 9 (x-4)

Step-by-step explanation:

which of the fractions 13/20, 3/5, 3/4 and 7/10 is greatest​

Answers

Answer:

3/4

Step-by-step explanation:

3/4

We can change all fractions to denominator 20 to easily vary them

13/20=13/20

3/5=12/20

3/4=15/20

7/10=14/20

What is an equation of the line that passes through the points (-4,-4) and (4,6), answer in fully reduced form.

Answers

Use  

y

2

y

2

x

2

x

1

4

9

2

3

=  

5

1

=

5

Answer link

Jim G.

Jun 11, 2018

y

=

5

x

6

Explanation:

the equation of a line in  

slope-intercept form

is.

x

y

=

m

x

+

b

where m is the slope and b the y-intercept

to calculate m use the  

gradient formula

x

m

=

y

2

y

1

x

2

x

1

let  

(

x

1

,

y

1

)

=

(

2

,

4

)

and  

(

x

2

,

y

2

)

=

(

3

,

9

)

m

=

9

4

3

2

=

5

1

=

5

y

=

5

x

+

b

is the partial equation

to find b substitute either of the 2 given points

into the partial equation

using  

(

2

,

4

)

then

4

=

10

+

b

b

=

4

10

=

6

y

=

5

x

6

is the equation of lineAnswer:

Step-by-step explanation:

Use  

y

2

y

2

x

2

x

1

4

9

2

3

=  

5

1

=

5

Answer link

Jim G.

Jun 11, 2018

y

=

5

x

6

Explanation:

the equation of a line in  

slope-intercept form

is.

x

y

=

m

x

+

b

where m is the slope and b the y-intercept

to calculate m use the  

gradient formula

x

m

=

y

2

y

1

x

2

x

1

let  

(

x

1

,

y

1

)

=

(

2

,

4

)

and  

(

x

2

,

y

2

)

=

(

3

,

9

)

m

=

9

4

3

2

=

5

1

=

5

y

=

5

x

+

b

is the partial equation

to find b substitute either of the 2 given points

into the partial equation

using  

(

2

,

4

)

then

4

=

10

+

b

b

=

4

10

=

6

y

=

5

x

6

is the equation of line

I- JUST NEED THE ANSWERS TO THIS QUESTION

Answers

Answer:

Undefined

Step-by-step explanation:

Today, there were 3 students absent from the math class. Each students that attended school solved 17 equations in math class. At the end of the class the teacher told the students that together they solved 408 equations today. How many students are this class if no one is absent?

Answers

Answer:

27 students

Step-by-step explanation:

Number of students present in the math class:

408/17 = 24

Number of students in this class:

24 + 3 = 27

Help me please I need assistance!​

Answers

Answer:

84ft

Step-by-step explanation:

one side of the house is 14 units

since 1unit=6ft

Length of one side of her house= 14(6)=84ft

Use place value multiplication with powers of 10 or equivalent fractions to explain what is happening mathematically to the decimal points in the divisor and the dividend before dividing

Answers

Answer:

436.8 x 100 / 62.08 x 100 = 43680/6208

Step-by-step explanation:

When you write the problem as a fraction, multiply the numerator and denominator by 100.  Multiplying each by 100 resulted in both numbers being whole numbers. 436.8/62.08 is the same as 43,680/6,208.

Please, help me with my homework! Thank you!

Answers

Answer:

i think (17)

Step-by-step explanation:

The perimeter of this compound shape (17) when you add up the sides and find the answer to the missing side.

3x + 1 = 3(x - 1) + 4​

Answers

Simplifying

3x + 1 = 3[x + -1] + 4

Reorder the terms:

1 + 3x = 3[x + -1] + 4

Reorder the terms:

1 + 3x = 3[-1 + x] + 4

1 + 3x = [-1 * 3 + x * 3] + 4

1 + 3x = [-3 + 3x] + 4

Reorder the terms:

1 + 3x = -3 + 4 + 3x

Combine like terms: -3 + 4 = 1

1 + 3x = 1 + 3x

Add '-1' to each side of the equation.

1 + -1 + 3x = 1 + -1 + 3x

Combine like terms: 1 + -1 = 0

0 + 3x = 1 + -1 + 3x

3x = 1 + -1 + 3x

Combine like terms: 1 + -1 = 0

3x = 0 + 3x

3x = 3x

Add '-3x' to each side of the equation.

3x + -3x = 3x + -3x

Combine like terms: 3x + -3x = 0

0 = 3x + -3x

Combine like terms: 3x + -3x = 0

0 = 0

This equation is an identity, all real numbers are solutions.

Identify the vertex of
y = 2x2 − 4x − 2

Answers

vertex at

(

1

,

4

)

Explanation:

Given:

y

=

2

x

2

+

4

x

2

Convert the given form into "vertex form"

y

=

m

(

x

a

)

2

+

b

with vertex at

(

a

,

b

)

XXX

y

=

2

(

x

2

+

2

x

)

2

complete the square

XXX

y

=

2

(

x

2

+

2

x

+

1

)

2

2

XXX

y

=

2

(

x

+

1

)

2

4

XXX

y

=

2

(

x

(

1

)

)

2

+

(

4

)

which is the vertex form with vertex at

(

1

,

4

)

graph{2x^2+4x-2 [-5.455, 7.034, -5.54, 0

The answer is (1,-4)

5x−7 = 3 help meee plz

Answers

Answer:

5x=3+7

5x=10

X=10/5

=2

what is 494 divided by 6.5

Answers

Answer:

76

Step-by-step explanation:

Answer:

494 divided by 6.5 =76

Step-by-step explanation:

Question 1) In an auditorium, there are 22 seats in the first row and 28 seats in the second row. The number of seats in a row continues to increase by 6 with each additional row. A) Write an iterative rule to model the sequence formed by the number of seats in each row. Show your work. (B) Use the rule to determine which row has 100 seats. Show your work. ( No Plagiarism and only answer if you know how to work this problem out. Will Mark Brainliest).​

Answers

Answer: Row 14

Step-by-step explanation:

Row 1= 22

Row 2= 28

Row 3= 34

Row 4= 40

Row 5= 46

Row 6= 52

Row 7= 58

Row 8= 64

Row 9= 70

Row 10= 76

Row 11= 82

Row 12= 88

Row 13= 94

Row 14= 100

This question is based on the sequence. Thus, the  row 14 has 100 seats.

Given:

In an auditorium, there are 22 seats in the first row and 28 seats in the second row. The number of seats in a row continues to increase by 6 with each additional row.

Now calculated the A part of the question.

According to the question,

By using iterative rule to model the sequence formed by the number of seats in each row.

Row 1= 22 Row 2= 28 Row 3= 34 Row 4= 40 Row 5= 46 Row 6= 52 Row 7= 58 Row 8= 64 Row 9= 70  Row 10= 76 Row 11= 82 Row 12= 88 Row 13= 94 Row 14= 100

(B) By using rule , we observe that row 14 has 100 seats.

For more details, prefer this link:

https://brainly.com/question/7854718

A glacier in Alaska moves about 29.9 meters a day. How much farther will it move in 1,000 days than in 100 days?|

Answers

The answer is 26,910 meters

Answer:

(1000x29.9)-(100x29.9)=29900-2990=26910

26910

Step-by-step explanation:

Can someone please help me with this question

Answers

Answer:

Eat some mc donolds then ur good

Step-by-step explanation:

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Can someone help me so stressed

29 points
Thanks

Answers

Answer:a square

Step-by-step explanation:a square

which graph represents the solution to this inequality

Answers

Answer:

C

Step-by-step explanation:

Answer

it is: C

Step-by-step explanation:

Find an equation for the line below

Answers

y = 6/9x + 1
Rise/run

Write the number below in expanded notation 75,966

Answers

7.596 to the 4th power

y
44
3
2-
-3
-2
2
3
4
-3+
-4
V
What is the slope of the line?

Answers

Answer:

-1

Step-by-step explanation:

-1 is the slope of the line

3) There were 35 children and 10 adults at a barbeque.
a. What is the ratio of adults to
children at the barbeque?
b. What is the ratio of children to
total people at the barbeque?
c. Five more children came to the
barbeque. Now what is the ratio
of children to total people?

Answers

Answer:

3. a. 10:35= 2:7

b.35:45=7:9

c.40:50=4:5

Henry decorates the top of each cupcake with 3 walnuts. If he has 56 walnuts, is that enough to decorate 2 dozen cupcakes? Why?

Answers

Answer:

No he does not have enough walnuts

Step-by-step explanation:

So if one dozen cupcakes is 12 then two dozen is 24 and each one has 3 walnuts and he only has 56 walnuts then what you have to do is multiply 24 by 3 and get 72 so the answer is no he does not have enough

Answer:

No, in order to decorate 2 dozen cupcakes(24) he needs 72 walnuts. With 56 he can only decorate 18 cupcakes.

Step-by-step explanation:

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