Question

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

x+5y=15
7x+2y=6

Answer 1

(0,3) One solution

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