Question

NEED HELP ASAP I HAVE 3 MINS

Answer 1

Explanation:

System of a equation has no solution when both the lines are parallel.

In other words, if the equations of a system have equal slopes there will be no solution.

1). x + 4y = 23

4y = -x + 23

`y=-(1)/(4)x+23` ------(1)

-3x = 12y + 1

12y = 3x - 1

`y=(1)/(4)x-(1)/(12)` -------(2)

Since, both the equations have different slopes, system will have at least one solution.

2). 2x + 4y = 22 -----(1)

-x = 2y - 11

-x - 2y = -11

x + 2y = 11

2x + 4y = 22 ------(2)

Since, both the equations are same, there will be infinite number of solutions.

3). 2x + y = 15 ------(1)

x = 15 - 2y

x + 2y = 15 -----(2)

Both the equations are different, therefore system of equations will have at least one solution.

4). 2x + y = 17 ------(1)

-4x = 2y - 34

-4x - 2y = -34

2x + y = 17 -----(2)

Both the equations are different, therefore, system of equations will have infinite solutions.

5). 3y = 10 - x

x + 3y = 10

2x + 6y = 20 -------(1)

2x + 6y = 7 ---------(2)

Since, both the lines are parallel (Same slopes), system will have no solution.

6). y = 13 - 2x ------(1)

4x - y = -1

-y = -4x - 1

y = 1 + 4x --------(2)

Since, both the equations are different, system of equations will have at least one solution.