(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

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

(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

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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 !

Michael F. | Mathematics TutorMathematics Tutor

(1) x=4y+3

2x+5y=-7

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

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

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

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

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