Problem solving - Linear Systems

Question

1) Solve the following linear system using Substitution and interpret the results.

6x=3y+2 and y-2x+4=0

2) Two fractions have denominators 3 and 4 and their sum is 17/12. If the numerators are switched, the sum is 3/2. Set up a linear system and solve it using Elimination to determine the two numerators.

Answer 1

6x=3y+2

y-2x+4=0

y=2x-4

substitute

6x=3(2x-4)+2

6x=6x-12+2

6x=6x-10

0=-10 false statement implies NO SOLUTION

x/3 + y/4 = 17/12

y/3 + x/4 = 3/2

y/3 + x/4 = 18/12

4x+3y=17

4y+3x=18

3x+4y=18

multiply first equation by 3, all terms

multiply second equation by 4, all terms

12x+9y=51

12x+16y=72

subtract first eq from second eq

7y=21

y=3

substitute to get x=2

I know that you need work but notice that 3 and 4 are relatively prime (no common factors except 1)

The LCD is 3*4=12

your answer is 17/12

what times 3 plus what times 4 equals 17 ?

not many options....

3*3+4*2=17

so y=3 and x=2