Does the system have one solution, no solution, or infinitly many? Use substitution to justify your answer

x+5y=15

7x+2y=6

(0,3) One solution

Step-by-step explanation:

Step: Solve x+5y=15for x:

x+5y=15

x+5y+-5y=15+-5y (Add - 5y to both sides)

x=-5y+15

Step: Substitute - 5y+15for x in 7x+2y=6:

7x+2y=6

7 (-5y+15) + 2y=6

-33y+105=6 (Simplify both sides of the equation)

-33y+105+-105=6+-105 (Add - 105 to both sides)

-33y=-99

-33y

-33

=

-99

-33

(Divide both sides by - 33)

y=3

Step: Substitute 3 for y in x=-5y+15:

x=-5y+15

x = (-5) (3) + 15

x=0 (Simplify both sides of the equation)

Therefore (0,3) which is one solution