# solve for x , y2x - 3y = -1 x+5y =7

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

Posted on

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 | College Teacher | (Level 3) Valedictorian

Posted on

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

x = 16/13,

y = 15/13

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 | 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

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).