Mathematics : asked on payton05

30.07.2021

Solve x/3+y/4=2
2x/3+3y/4=5

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09.07.2023, solved by verified expert

Rajat Thapa

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Mathematics, DAV Post Graduate College

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Solve x/3+y/4=2 2x/3+3y/4=5, №18011016, 30.07.2021 13:12

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Rajat Thapa

s Specialist

Mathematics, DAV Post Graduate College

4 214

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4.9 rating

Unlock the full answer

Step-by-step explanation:

8x + 9y = 60 -------------------------(ii)

Multiply equation (i) by (-2)

(i)*(-2) -8x -6y = -48

(ii) 8x +9y = 60 {Now add. x will be cancelled}

3y = 12 {Divide both sides by 3}

y = 12/3

y = 4

Substitute y = 4 in equation (i)

4x + 3*4 = 24

4x + 12 = 24

4x = 24 - 12

4x = 12

x = 12/4

x = 3

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Mathematics

Solve x/3+y/4=2 2x/3+3y/4=5

Step-by-step answer

P Answered by Master

Step-by-step explanation:

please mark me as brainlest

Mathematics

Systems of Linear Equations What are the different ways to solve a system of linear equations? When do you get an answer to a system of linear equations that has one solution, no solution and infinitely many solutions? Solve each of the following systems by graphing. y = -x – 7 y = 4/3 x – 7 y = -3x – 5 y = x + 3 y = -2x + 5 y = 1/3 x – 2 3x + 2y = 2 x + 2y = -2 x + 3y = -9 2x – y = -4 x – 2y = 2 -x + 4y = -8 5x + y = -2 x + y = 2

Step-by-step answer

P Answered by PhD

Different ways to solve a system of linear equations:

isolate one variable in one equation and replace it in the other equationmultiply/divide one equation by a constant and then add/subtract it to the other one, so that only one variable remainsgraph the equation and look at the intersection point

If you graph the system:

there is only one solution if the lines intersects at only one pointthere is no solution if the lines don't intersect each other (they are parallel)there are infinitely many solutions if the lines overlap each other (they are the same equation multiplied by some constant)

Step-by-step explanation:

1st system

y = -x – 7

y = 4/3 x – 7

solution: x= 0, y = 7

2nd system

y = -3x – 5

y = x + 3

solution: x = -2, y = 1

3rd system

y = -2x + 5

y = 1/3 x – 2

solution: x = 3, y = -1

4th system

3x + 2y = 2

x + 2y = -2

solution: x = 2, y = -2

5th system

x + 3y = -9

2x – y = -4

solution: x = -3, y = -2

6th system

x – 2y = 2

-x + 4y = -8

solution: x = -4, y = -3

7th system

5x + y = -2

x + y = 2

solution: x = -1, y = -3

Systems of Linear Equations What are the different ways to solve a system of linear equations? When

Mathematics

Step-by-step answer

P Answered by PhD

Different ways to solve a system of linear equations:

If you graph the system:

Step-by-step explanation:

1st system

y = -x – 7

y = 4/3 x – 7

solution: x= 0, y = 7

2nd system

y = -3x – 5

y = x + 3

solution: x = -2, y = 1

3rd system

y = -2x + 5

y = 1/3 x – 2

solution: x = 3, y = -1

4th system

3x + 2y = 2

x + 2y = -2

solution: x = 2, y = -2

5th system

x + 3y = -9

2x – y = -4

solution: x = -3, y = -2

6th system

x – 2y = 2

-x + 4y = -8

solution: x = -4, y = -3

7th system

5x + y = -2

x + y = 2

solution: x = -1, y = -3

Mathematics

Which pair of lines is perpendicular? a. y=2x-1 and 2y=-x+3 b. y=3x+4 and 3y-x=5 c. y=-4x+2 and x+4y=6 d. y=-6x-3 and 6x-y=4

Step-by-step answer

P Answered by Specialist

The answer to this is A. y=2x-1 and 2y=-x+3

Mathematics

Can someone answer these for me? ill give brainliest, i really need to finish : ( (substitution method) 1) -8x+2y=-4 y=-3x-2 2) 12x-3y=4 y=4x 3) 3x+2y=11 x+2y=9 4) -3+2y=5 -4x+y=10

Step-by-step answer

P Answered by PhD

Step-by-step explanation:

-8x + 2y = -4 12x - 3y = 4

y = -3x - 2 y = 4x

sub sub

-8x + 2(-3x - 2) = -4 12x - 3(4x) = 4

-8x - 6x - 4 = -4 12x - 12x = 4

-14x = -4 + 4 0 = 4

-14x = 0 NO SOLUTION

x = 0

y = -3x - 2 -3 + 2y = 5

y = -3(0) - 2 -4x + y = 10...y = 4x + 10

y = -2 sub

solution is : (0,-2) -3 + 2(4x + 10) = 5

-3 + 8x + 20 = 5

3x + 2y = 11 8x + 17 = 5

x + 2y = 9...x = 9 - 2y 8x = 5 - 17

sub 8x = - 12

3(9 - 2y) + 2y = 11 x = -12/8

27 - 6y + 2y = 11 x = -3/2

-4y = 11 - 27

-4y = -16 y = 4x + 10

y = -16/-4 y = 4(-3/2) + 10

y = 4 y = -12/2 + 10

y = -6 + 10

x = 9 - 2y y = 4

x - 9 - 2(4) solution (-3/2,4)

x = 9 - 8

x = 1

solution : (1,4)

Mathematics

Can someone answer these for me? ill give brainliest, i really need to finish : ( (substitution method) 1) -8x+2y=-4 y=-3x-2 2) 12x-3y=4 y=4x 3) 3x+2y=11 x+2y=9 4) -3+2y=5 -4x+y=10

Step-by-step answer

P Answered by PhD

Step-by-step explanation:

-8x + 2y = -4 12x - 3y = 4

y = -3x - 2 y = 4x

sub sub

-8x + 2(-3x - 2) = -4 12x - 3(4x) = 4

-8x - 6x - 4 = -4 12x - 12x = 4

-14x = -4 + 4 0 = 4

-14x = 0 NO SOLUTION

x = 0

y = -3x - 2 -3 + 2y = 5

y = -3(0) - 2 -4x + y = 10...y = 4x + 10

y = -2 sub

solution is : (0,-2) -3 + 2(4x + 10) = 5

-3 + 8x + 20 = 5

3x + 2y = 11 8x + 17 = 5

x + 2y = 9...x = 9 - 2y 8x = 5 - 17

sub 8x = - 12

3(9 - 2y) + 2y = 11 x = -12/8

27 - 6y + 2y = 11 x = -3/2

-4y = 11 - 27

-4y = -16 y = 4x + 10

y = -16/-4 y = 4(-3/2) + 10

y = 4 y = -12/2 + 10

y = -6 + 10

x = 9 - 2y y = 4

x - 9 - 2(4) solution (-3/2,4)

x = 9 - 8

x = 1

solution : (1,4)

Mathematics

What is the value of 12x^-3y^-1 for x=-1 and y=5? 1. -12/5 2. -180 3. -60 4. -5/12

Step-by-step answer

P Answered by PhD

ANSWER

$- \frac{12}{5}$

EXPLANATION

The given expression is

$12 {x}^{ - 3} {y}^{ - 1}$

We can rewrite as positive index to get,

$\frac{12}{ {x}^{3} } \times \frac{1}{y}$

$= \frac{12}{ {x}^{3}y}$

We substitute x=-1 and y=5.

$= \frac{12}{( { - 1}^{3}) \times 5 }$

$= \frac{12}{ - 5} = - \frac{12}{5}$

Mathematics

What is the value of 12x^-3y^-1 for x=-1 and y=5? 1. -12/5 2. -180 3. -60 4. -5/12

Step-by-step answer

P Answered by PhD

ANSWER

$- \frac{12}{5}$

EXPLANATION

The given expression is

$12 {x}^{ - 3} {y}^{ - 1}$

We can rewrite as positive index to get,

$\frac{12}{ {x}^{3} } \times \frac{1}{y}$

$= \frac{12}{ {x}^{3}y}$

We substitute x=-1 and y=5.

$= \frac{12}{( { - 1}^{3}) \times 5 }$

$= \frac{12}{ - 5} = - \frac{12}{5}$

Mathematics

15 points can someone check my answers? 1. for the data in the table, does y vary directly with x? if it does write an equation for the direct variation.(x,y) (8,11) (16,22) (24,33) yes y=2.75x yes y=0.6875x*** yes y=1.375x no y does not vary directly with x ** (for #1, i m debating between b and d) 2.for the data in the table, does y vary directly with x? if it does write an equation for the direct variation. (x,y) (16,4) (32,16) (48,36) yes y=2x yes y=4x yes y=8x no y does not very directly with x*** 3. (time/hour,distance/miles)(4,233) (6,348)

Step-by-step answer

P Answered by PhD

2 and 9 are correct. The remainder need to be reconsidered.

Step-by-step explanation:

Your answer to 9 is correct, which means you have the appropriate signs for the point coordinates. In your other point-slope questions, one or more of the signs is incorrect. Use your good work as an example of how to choose the correct answers elsewhere.

1) When you have y = kx, you can find the value of k from ...

... k = y/x

When the variation is direct, this works for any (x, y) pair.

3) A unit rate is called a unit rate because it has 1 (a unit) in the denominator.

4a, 4b, ... all slope calculations. You managed to get it right in problem 9. Watch your signs.

10, 11 ... It can work well to put the x term on the same side with the y-term, then multiply the equation by the denominator value.

... (2/3)x + y = 7 . . . . add (2/3)x to both sides of the equation

... 2x + 3y = 21 . . . . . multiply by 3. (Standard form always has the leading coefficient positive.)

Whenever you consider making a term disappear from one side of the equation, think in terms of adding its opposite to both sides of the equation. This will give the result you want and is consistent with the properties of equality: whatever you do to one side of the equation you must also do to the other side of the equation. Other wording may have been used by your teacher or friends. This is the one true statement about transforming equations.

Mathematics

Step-by-step answer

P Answered by PhD

1. y varies directly with x and the equation is y=1.375x

2. No, y does not vary directly with x

3. Your car travels 58 miles in 1 hour

4. $-\frac{1}{3}$

5. $-\frac{26}{27}$

6. y-2=3(x-5)

7. $y+5=-\frac{2}{5}(x+3)$

8. y+7=-0.54(x-4)

9. y-16=8(x-2)

10. 2x+3y=21

11. x+2y=2

Step-by-step explanation:

For to vary directly with , all the 3 pair of numbers need to show the same ratio if we divide each y's by the x's. Let's check.

$\frac{11}{8}=1.375$ $\frac{22}{16}=1.375$ $\frac{33}{24}=1.375$

So all of them show the same ratio and hence y varies directly with x.

For equation, we already saw that multiplying x by 1.375 gives us y. We can write in equation form as:

y=1.375x

Third answer choice is correct.

This is similar to #1. So let's check the ratios.

$\frac{4}{16}=0.25$ $\frac{16}{32}=0.5$ $\frac{36}{48}=0.75$

As we can see, the ratios are not equal to y does not vary directly with x.

Fourth answer choice is correct.

The first number in the pair gives time and second number gives distance. To get unit rate, we divide the distance by time. So we will get the number of miles traveled in 1 hour.

$\frac{233}{4}=58.25$ [ i believe this is a typo and it should be 232 miles and ratio would be 58 ]

$\frac{348}{6}=58$

$\frac{464}{8}=58$

$\frac{580}{10}=58$

As we can see, in 1 hour, distance covered is 58 miles. Third answer choice is right.

If the 2 points are taken as $(x_{1},y_{1})$ and $(x_{2},y_{2})$

And we know formula of slope to be:

$\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$

The slope of the line is:

$\frac{3-5}{8-2}=\frac{-2}{6}=-\frac{1}{3}$

The slope of the line is $-\frac{1}{3}$

Second answer choice is correct.

4. [this should be #5]

If the 2 points are taken as $(x_{1},y_{1})$ and $(x_{2},y_{2})$

And we know formula of slope to be:

$\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$

The slope of this line can be found now:

$\frac{2.7-8.7}{-3.2-(-5.2)}=\frac{2.7-8.7}{-3.2+5.2}=\frac{-6}{2}=-3$

The slope of the line is

Fourth answer choice is correct.

The formula of slope is:

$\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$

Where,

the 2 points are taken as $(x_{1},y_{1})$ and $(x_{2},y_{2})$

Now finding the slope:

$\frac{\frac{7}{3}-(-2)}{-3-\frac{3}{2}}=\frac{\frac{7}{3}+2}{-\frac{9}{2}}=\frac{\frac{13}{3}}{-\frac{9}{2}}=-\frac{26}{27}$

The slope of the line is $-\frac{26}{27}$

Second answer choice is right.

Point Slope form of a line is given as:

$y-y_{1}=m(x-x_{1})$

Where,

$(x_{1},y_{1})$ is the point given, andm is the slope

Using the point (5, 2) and slope as 3 given, we can write the equation:

y-2=3(x-5)

Fourth answer choice is right.

Point Slope form of a line is given as:

$y-y_{1}=m(x-x_{1})$

Where,

$(x_{1},y_{1})$ is the point given, andm is the slope

Using the point given as (-3,-5) and slope as $m=-\frac{2}{5}$ , we can write the point slope form of the equation as:

$y-(-5)=-\frac{2}{5}(x-(-3))\\y+5=-\frac{2}{5}(x+3)$

First answer choice is right.

Point Slope form of a line is given as:

$y-y_{1}=m(x-x_{1})$

Where,

$(x_{1},y_{1})$ is the point given, andm is the slope

The slope is given as -0.54 and the point is (4, -7). So the point slope form is:

$y-(-7)=-0.54(x-4)\\y+7=-0.54(x-4)$

First answer choice is right.

In this question, we can just have a quick look and see that the -coordinate is 8 times the -coordinate. So we can say that y=8x

Expanding the equations below would tell us which one is equal to that. Let's check.

$y-16=8(x-2)\\y-16=8x-16\\y=8x-16+16\\y=8x$

This is the correct one.

So first answer choice is right.

10.

The standard form of the equation of a line is given as:

Ax+By=C

Rearranging the given equation gives us:

$y=-\frac{2}{3}x+7\\\frac{2}{3}x+y=7$

Now, we can't have a fraction, so we multiply all of it by 3 to get rid of the denominator. Now we have:

$3*(\frac{2}{3}x+y=7)\\2x+3y=21$

First answer choice is right.

11.

The standard form of a line is Ax+By=C

Rearranging the given equation, we have:

$y=-\frac{1}{2}x+1\\\frac{1}{2}x+y=1$

We cannot have fractions, so we multiply the whole thing by 2 to get rid of the denominator. So we have:

$2*(\frac{1}{2}x+y=1)\\x+2y=2$

First answer choice is correct.

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Solve x/3+y/4=2 2x/3+3y/4=5

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