Answer:
(6,-7)
(2,1)
(-4,13)
Step-by-step explanation:
we have
[tex]2x+y=5[/tex] -----> equation A
[tex]3y=15-6x[/tex] ----> equation B
Multiply the equation A by 3 both sides
[tex]3(2x+y)=3(5)[/tex]
[tex]6x+3y=15[/tex]
isolate the variable 3y
[tex]3y=15-6x[/tex] -----> equation C
equation B and equation C are equal
That means -----> is the same line
so
The system has infinity solutions
Remember that
If a ordered pair is a solution of the line, then the ordered pair must satisfy the equation of the line
Verify each ordered pair
1) (6,-7)
substitute the value of x and the value of y in the linear equation
[tex]3(-7)=15-6(6)[/tex]
[tex]-21=-21[/tex] ---> is true
so
The ordered pair is a solution of the system of equations
2) (2,1)
substitute the value of x and the value of y in the linear equation
[tex]3(1)=15-6(2)[/tex]
[tex]3=3[/tex] ---> is true
so
The ordered pair is a solution of the system of equations
3) (-2,-9)
substitute the value of x and the value of y in the linear equation
[tex]3(-9)=15-6(-2)[/tex]
[tex]-27=27[/tex] ---> is not true
so
The ordered pair is not a solution of the system of equations
4) (-4,13)
substitute the value of x and the value of y in the linear equation
[tex]3(13)=15-6(-4)[/tex]
[tex]39=39[/tex] ---> is true
so
The ordered pair is a solution of the system of equations
