solve for x , y2x - 3y = -1 x+5y =7

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hala718's profile pic

hala718 | High School Teacher | (Level 1) Educator Emeritus

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2x- 3y = -1......(1)

x+5y = 7........(2)

Using the substituting method:

Rewrite (2);

x= 7- 5y

Now substitute n (1)

2x-3y = -1

2(7-5y) - 3y = -1

14 - 10y -2y = -1

12y = 15

==> y = 15/12 = 5/4

==> y= 5/4

==> x= 7-5y = 7-5(5/4)

           = 7- 25/4 = 28-25/4 = 3/4

==> x= 3/4

krishna-agrawala's profile pic

krishna-agrawala | College Teacher | (Level 3) Valedictorian

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2x - 3y = -1   ...   (1)

x + 5y = 7   ...   (2)

Multiplying equation (2) by 2:

2x + 10y = 14   ...   (3)

Subtracting equation (1) from equation (3):

2x - 2x + 10y + 3y = 14 + 1

==> 13y = 15

Therefore:

y = 15/13

Substituting this value of y in equation (2):

x + 5*(15/13) = 7

==> x + 75/13 = 7

==> x = 7 - 75/13 = 16/13

Answer:

x = 16/13,

y = 15/13

giorgiana1976's profile pic

giorgiana1976 | College Teacher | (Level 3) Valedictorian

Posted on

Because the equations of the system are linear, we'll use the matrix formed by the coefficients of the variables to calculate the determinant of the system:

             2        -3

det A =

             1         5

 

det A = 10+3 = 13

det A = 13 different from zero.

Now, we'll calculate x:

x = det x/ det A

             -1         -3

det x =

             7         5

 

det x = -5 - 21 = -26

x = -26/13

x = -2

Now, we'll calculate y:

 

             2         -1

det y =

             1         7

det y = 14-1

det y =15

 

y = det y/ det A

y = 15/13

y = 15/13

The solution of the system is: {(-2 , 15/13)}

thewriter's profile pic

thewriter | College Teacher | (Level 1) Valedictorian

Posted on

Given 2x-3y=-1 and x+5y=7 we have to find x and y.

2x-3y=-1                           ...(1)

x+5y=7                             ...(2)

Multiply (2) by 2 and subtract (1). We get

2x+10y-2x+3y=14-(-1)

=>13y=15

=>y=15/13

Substituting y=15/13 in (2) we get

x+5*(15/13)=7 or x=7-45/13 or x=(91-75)/13=16/13

Therefore x=16/13 and y=15/13

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neela | High School Teacher | (Level 3) Valedictorian

Posted on

2x-3y = -1....(1)

x+5y = 7.......(2)

Solution:

We can eliminate x by  Eq(1) -2*(2) and solve for y:

(2x-3y) -2(x+5y) = -1-2*7

-3y-10y =  -1-14 = -15

-13y =-15.

y = -15/-13 = 15/13

We can eliminate y by the operation  5*Eq(1) +3*Eq(2):

5(2x-3y)+3(x+5y) = 5*(-1)+3*7 = 16

10x+3x =16

13x=16

13x/13 = 16/13

x = 16/13

So (x,y) = (16/13 , 15/13).

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