Question

Solve the system:

x/3 + 4y/3 = 100
3x - 4y = 100

(A) {0, -25}
(B) {50, 12.5}
(C) {50, 100}
(D) {100, 50}

Q: How would i solve this? Please explain it out completely, thanks.

Answer 1

{ x/3 + 4y/3 = 10
  3x - 4y = 100

isolate x for x/3 + 4y/3 = 100

Multiply both sides by 3 :

x/3 * 3 +4y/3 * 3 = 100 * 3

refine : x + 4y = 300

subtract 4y from  both sides:

x + 4y - 4y = 300 - 4y

refine :  x = 300 - y

subsititute   x = 300 - y
 
[ 3(300 - 4y ) - 4y = 100 ]

900 - 16y  - 900 = 100 - 900

- 16 y = - 800

y = - 800 / - 16

y =  50

for x  = 300 -y :

subsititute  y = 50

x = 300 - 4 * 50

x = 300 - 200

x = 100 

the solutions to the system equations are :

x =  100 , and y = 50

Answer D

hope this helps!