Solve for x and y by any method(show work)?

Question

If there is no solution then simply put no solution.

1. x-5y=6
3x-2y=5

2. 6x+y=2
2x-y=-2

Answer 1

-3x+15y = -18
3x - 2y = 5
13y = -13 so y=-1
Now x-5y =-18 therefore x+5 = -18
x= -18-5
x= -23 Ans (-23,-1)

6x+y = 2
2x -y = 2
8x = 4
x = 4/8
x=0.5
Now
6x+y =2
So 3+y = 2
y = 2-3
y = -1
Checking in 2nd eq:
2x-y=2 and x=0.5 and y=-1
if 1+1 = 2 True

Answer 2

I'll show you two methods for solving simultaneous equations.

1. Rewrite both equations so
(a)  x is isolated on one side of the equals sign
(a)  the coefficient of x is 1

Add 5y to both sides of x - 5y = 6:
     x = 6 + 5y

Add 2y to both sides of 3x - 2y = 5:
     3x = 5 + 2y
Divide both sides by 3:
     x = 5/3 + (2/3)y

Combine the two new equations to eliminate the x terms:
     x = 6 + 5y
     x = 5/3 + (2/3)y
so
     6 + 5y = 5/3 + (2/3)y
Solve for y:
     (5 - 2/3)y = 5/3 -6
     (13/3)y = -13/3
     y = -1

     x = 6 + 5y = 1
Solution = (1,-2)

2. Second method is to scale one equation so the coefficient of x is the same in both equations.

     6x + y = 2
     2x - y = -2

Multiply the second equation by 3 so the coeff. of x is 6:
     3(2x - y = -2)
     6x - 3y = -6

Subtract one equation from the other (it doesn't matter which) to eliminate the x terms:

     6x +  y = 2
  - (6x - 3y = -6)
     ---------------
             4y = 8
               y = 2

Use value of y to solve for x:
     2x - 2 = -2
     x = 0

Answer 3

I think the easiest would be substitution for no. 1 and addition for no. 2.

1. x = 6 + 5y


Substituting:

3(6 + 5y) - 2y = 5
18 + 15y - 2y = 5
13 = -13y
y = -1
x = 1


2. 6x + y =2
2x - y = -2


Add
8x = 0
x = 0
y = 2

Answer 4

The easiest way to solve is by substitution

x-5y=6
3x-2y=5

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

18+15y-2y=5
18+13y=5
13y=-13
y=-1
x-5(-1)=6
x+5=6
x=1
x=1 y=-1

6x+y=2
2x-y=-2

y=-6x+2

2x-(-6x+2)=-2
2x+6x-2=-2
8x-2=-2
8x=0
x=0/8=0

2(0)-y=-2
0-y=-2
-y=-2
y=2

x=0 y=2

Answer 5

(1) x - 5y = 6

add 5y to both sides .... we are solving for 'x'

x - 5y + 5y = 6 + 5y

x = 6 + 5y.............equation (1)

Now , put the value of 'x' in equation (2) which is ..
3x - 2y = 5................equation (2)

3( 6 + 5y) - 2y = 5..........after putting value of 'x' from equation (1)

Now distribute 3 to all the elements in inside the bracket

18 + 15y - 2y = 5

18 + 13y = 5 ( .... +15 y -2y = 13y)

18 -18 + 13y = 5 - 18.....(Subtracting 18 from both sides)

13y = -13 ( since ... 5 -18 = -13)

Divide both sides by 13 ....we have

13y / 13 = -13 /1 3

y = -1 ......answer ...


Similarly . you can solve for the second question .....

Regards,
Abhishek
Algebra Tutor ..(www.eduwizards.com)

Answer 6

Ans 1.x-5y=6...........Eq.1
3x-2y=5...............Eq.2
Multiply Eq.1 by 3,u will get,
3x-15y=18.......Eq.3
Subtract Eq.2 from Eq.3,u will get,
-13y=13
y = -1
Substituting y = -1 in Eq.1,u will get,
x -5(-1) = 6
x+5 = 6
x= 1

Ans.2. 6x+y=2.........Eq.1
2x-y= -2............Eq.2
Adding Eq.1 and Eq.2,
8x=0
x=0
Substituting x=0 in Eq.1,
6(0) + y=2
0+y=2
y=2