Question

Need help with this....
Solve the following system of equations using the substitution method.
x+3y=10
xy= 7

Answer 1

Isolate one of the variables in one of the equations. I suggest x in the first equation

x+3y = 10

subtract 3y from both sides

x = 10-3y

now substitute this x in the second equation

xy = 7 becomes (10-3y) y = 7

expand

10y - 3y^2 = 7

subtract 7 from both sides

10y - 3y^2 - 7 = 0

multiply by -1

3y^2 -10 y + 7 = 0

Factor:

(3y-7) (y-1) = 0

y = 7/3 or 1

Plug these into the original equation

x = 10-3y x = 3 or x = 7

Answer 2

x+3y=10
x = 10 -3y

SUB INTO NEXT EQUATION

(10 - 3y)y = 7
10y - 3y^2 -7 = 0
-3y^2 +10y - 7 = 0

FACTOR

Answer 3

Thank you! I understand it now.