Method of Substitution

Question

Solve the system by the method of substitution. (If there is no solution, enter NO SOLUTION.)

1/5x+1/2y=8 x+y=20 Now I have gotten several different solutions, the last one was -5,25 BUT apparently that was wrong. Could I get some help on this?

Answer 1

(1/5)x + (1/2)y = 8

x + y = 20

multiplies first equation by 10 to clear away the fractions;

multiplies second equation by -2

2x + 5y = 80

-2x + -2y = -40

3y = 40

y = 40/3

substitutes into original second equation:

x + 40/3 = 20

3x + 40 = 60

3x = 20

x = 20/3

CHECKS with original first equation:

(1/5)(20/3) + (1/2)(40/3) =

20/15 + 40/6 = <-- multiplies the fractions

40/30 + 200/30 = <-- LCD is 30

240/30 = 8 <-- yes it checks

the solution is (x=20/3, y = 40/3)