HELP ME OUT PLEASE SOLVE IT

Question

Solved the system by substitution.if the system is inconsistent and has no solution,state this .if the system is dependent,write the form of the solution for any real number x.

(1) x=4y+3
2x+5y=-7

(2) x=-2/3y+3/4
12x+8y=6

(3)y=5x+2
y=9x-6

(4)2x-y=-15
5x+6y=5

Answer 1

1) x=4y+3

   2x+5y=-7

   2(4y+3)+5y=-7

   8y+6+5y=-7

   13y+6=-7

   13y=-6-7

   13y=-13

      y=-1

    x=4(-1)+3

    x=-4+3

    x=-1

  (-1,-1)

check: 2(-1)+5(-1)=-7

             -2+(-5)=-7

                      -7=-7

          

            -1=4(-1)+3

            -1=-4+3

            -1=-1

  4) 2x-y=-15

      5x+6y=5

    

     2x-y=-15

        -y=-2x-15

         y=2x+15

      substitute now

        5x+6(2x+15)=5

        5x+12x+90=5

        17x+90=5

        17x=-85

           x=-5

        5x+6y=5

       5(-5)+6y=5

         -25 +6y=5

              6y=30

               y=5

  solution: (-5,5)     

 

You try 2) and 3) !    

Good Luck !

 

Answer 2

(1) x=4y+3
2x+5y=-7

rewrite as

   x-4y=3

2x+5y=-7

multiply the first equation by 2 to get

2x-8y=6 and now write the second

2x+5y=-7

Subtract the second equation from the first to get

-13y=13or that y=-1

substituting this in, say, x-4y=3 we get x-4(-1)=3

or x=-1

Verify as -1+4=3 or as 2(-1)+5(-1)=-2-5=-7

 

(2) x=-2/3y+3/4
12x+8y=6

rewrite as

x+2/3y=3/4

12x+8y=6

Multiply the first equation by 12 to get

12x+8y=9

It is not possible for 12x+8y=6 and 12x+8y=9 at the same time.

These equations are of two parallel lines with no points in common.  There are no solutions.

 

(3)y=5x+2
y=9x-6

These two equations give that 5x+2=9x-6 since both are equal to y

subtract 5x from both sides to get 2=4x-6, add 6 to both sides to get

8=4x or that x=2.  Substituting in either equation say the first y=5(2)+2=12

or the second y=9(2)-6=12

 

(4)2x-y=-15
5x+6y=5

Rewrite to align the equations as

2x   -y=-15

5x+6y=5

Multiply the first equation by 6 to get

12x-6y=-90  the second written below is

5x+6y=5

Add to get

17x=-85 or that x=-5

Substitute in the first equation to get

2(-5)-y=-15 which gives -10-y=-15 or that -y=-5 or y=5

The second equation can be used to verify this result as 5(-5)+6(5)=5