Please solve this problem.                    Y - 1 = _ 3                  _____    ____                   x + 3        4

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justaguide's profile pic

justaguide | College Teacher | (Level 2) Distinguished Educator

Posted on

The equation `(y -1)/(x+3) = 3/4` has to be solved.

The given equation has 2 variables y and x. As only a single equation is provided it is not possible to determine a unique solution for the two variables. Each of the variables can be defined as an expression of the other.

`(y -1)/(x+3) = 3/4`

=> `y - 1 = (3/4)*(x + 3)`

=> `y = (3/4)*(x + 3) + 1`

=> `y = (3x)/4 + 9/4 + 1`

=> y = `(3x)/4 + 13/4`

This defines y in terms of x

`(y -1)/(x+3) = 3/4`

=> `x + 3 = (4/3)(y - 1)`

=> `x = (4y)/3 - 4/3 - 3`

=> `x = (4y)/3 - 13/3`

This defines x in terms of y.

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Jyotsana | Student, Grade 10 | (Level 1) Valedictorian

Posted on

4(y-1)=-3(x+3)

4y-4=-3x-9

4y-4+3x=-3x-9

4y-4+3x+4=-9+4

4y+3x=-5

4y+3x=-5

4y+3x-3x=-5-3x

4y=-5-3x

4y/4=-5/4-3x/4

y=-1.25-0.75x

4y+3x=-5

4y+3x-4y=-5-4y

3x=-5-4y

3x/3=-5/3-4/3y

x=-5/3-4/3y

Jyotsana's profile pic

Jyotsana | Student, Grade 10 | (Level 1) Valedictorian

Posted on

4(y-1)=-3(x+3)

4y-4=-3x-9       to find y  

4y-1+1=-3x-9+1  add 1 on both side

4y/4= (-3x-8)/4

y= -3/4x-2

4y-4= -3x-9    to find x

4y-4+9= -3x-9+9    add 9 on both side

(4y+5)/-3= -3x/-3

4/-3y+5/-3=x    

adarshanurag's profile pic

adarshanurag | Student, Grade 11 | (Level 1) Valedictorian

Posted on

Your question is not clear. Minimum 2 equations are needed to solve x and y. Different answers you need are:-

(y-1)/(x+3) = -3/4

=> 4(y-1) = -3(x+3)

=> 4y-4 = -3x-9

=> 4y+3x = -5

This is the equation if you need it.

If you want x in terms of y:-

4y+3x = -5

=>3x = -5-4y

=>x= -(5+4y)/3

If you want y in terms of x:-

4y+3x = -5

=> 4y = -3x-5

=> y = -(3x+5)/4

nicole8923's profile pic

nicole8923 | Student, Grade 10 | (Level 1) Salutatorian

Posted on

4(y-1)=-3(x+3)

4y-4=-3x-9       to find y  

4y-1+1=-3x-9+1  add 1 on both side

4y/4= (-3x-8)/4

y= -3/4x-2

4y-4= -3x-9    to find x

4y-4+9= -3x-9+9    add 9 on both side

(4y+5)/-3= -3x/-3

4/-3y+5/-3=x    

gturner49's profile pic

gturner49 | (Level 1) Honors

Posted on

I don't have an answer.  I have another question.  In the original equation, the 3/4 is negative.  Does that change the solution in any way?  I didn't see the negative sign in your solution.

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justaguide's profile pic

justaguide | College Teacher | (Level 2) Distinguished Educator

Posted on

A negative sign does alter the final expressions derived for x and y in terms of y and x respectively.

Though it is not possible to solve a set of equations unless the number of variables is equal to the number of independent equations given.

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