Question

Select whether each system of equations has no solution, one solution, or infinitely many solutions.

No Solution

One Solution

Infinitely Many Solutions



x + 2y = 6

2x − 3y = 26




4x − 2y =−6

y = 2x − 4




2x − y = 4

6x − 3y = 12
Select whether each system of equations has no solution, one solution, or infinitely many solutions.



No Solution

One Solution

Infinitely Many Solutions



x + 2y = 6

2x − 3y = 26




4x − 2y =−6

y = 2x − 4




2x − y = 4

6x − 3y = 12

Answer 1

one solution, no solution, infinitely many solutions

Explanation:

I rearranged the first equation into x=6-2y

plug that into the second equation

2(6-2y)-3y=26

12-4y-3y=26

12-7y=26

-7y=14

y=-2

Then you plug that into one of the equations

x+2(-2)=6

x-4=6

x=10

The solution to the first system is (10,-2)

the second system already has one equation as something equal to a single variable so you just plug that into the other one

4x-2(2x-4)=-6

4x -4x +8 =-6

8=-6

this is a false statement so the system of equation has no solution

Lastly I rearranged the first equation into y=2x-4 and then plug that in

6x-3(2x-4)=12

6x-6x+12=12

12=12

this statement is true so the system of equations has infinite solutions