Arrange the systems of equations that have a single solution in increasing order of x-values in their solutions. 2x+y=10 x-3y=-2 2x + y= 10 -6x -3y=-2 x+2y= 5 2x + y = 4 5x+ y= 33 x=18-4y y=13 -2x 8x + 4y =52 x+ 3y =5 6x-y=11 y=10 + x 2x + 3y =45

(III), (VI),(VII), (I), (IV)

Step-by-step explanation:

Solving the system of equations one by one by elimination method

(I) 2x+y=10

   x-3y= -2   ( multiply by 2)

we have unique solution

x=4, y=2

(II) 2x+y=10    (multiply by -3)

 -6x-3y= -2

No solution.

(III) x+2y=5   (multiply by 2)

    2x+y=4

Unique solution

x=1, y=2

(IV) 5x+ y= 33

     x=18-4y ---> x+4y=18    (multiply by 5)

Unique solution

x=6, y=3

(V) Y=13 -2x   > 2x+y=13     ( multiply by 4)

   8x + 4y =52

No solution

(VI) x+ 3y =5

    6x-y=11    (multiply by 3)

Unique solution

x=2, y=1

(VII) Y=10 + x    > -x+y=10   (multiply by 2)

      2x + 3y =45

Unique solution

x=3 , y=13

Values of x in increasing order= (III), (VI),(VII), (I), (IV)

set each factor equal to 0

4x-3 = 0

2x-1 = 0

solve for x.

4x-3=0

4x=3

x= 3/4

solve for x. 

2x-1= 0

2x= 1

x= 1/2

your answer should be 1/2 is less than or equal to x and 3/4 is greater than or equal to x