Question

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

Answer 1

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

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)