Solve 3 system equations

Is (1, 1, 1) a solution to x+y+z=3 2x-y+4z=5 x+4y=3 ?

Yes 1+1+1=3 2-1+4=5 1+4-2=3

Annette sold $120 more than Barb x= Annette y= Barb

x= y + 120

Barb & Carlita combined sold $280 more than Annette x= Annette y= Barb z= Carlita

y + z = 280 + x

20 fewer roses than daisies y= roses z= daisies

y= z - 20

4x + 2y + 3z=1 2x - 3y +5z=-14 6x - y +4z=-1

1. Choose two equations to cancel out one variable: x, y or z: 4x + 2y + 3z=1 & 2x - 3y +5z=-14. 2. You will get a equation: 8y - 7z=29. 3. Choose another different two equations cancel out the same variable: 2x - 3y +5z=-14 & 6x - y +4z=-1. 4. You will get 8y - 11z=41. 5. Solve the two equations that you got from solving the equations: 8y - 7z=29 & 8y - 11z=41. 6. You will get the answer to z. 7. Plug in the answer to z to the equation that you solved using the problem equations: 8y - 7z=29 & 8y - 11z=41. 8. You will get the answer to y. 9. Plug in the answer to y & z to one of the three problem equations: 4x + 2y + 3z=1, 2x - 3y +5z=-14 or 6x - y +4z=-1.

Steps to solve 3 system equations

1. Rewrite 2. Solve 3. Substitute

If the solution is: 0=0

Infinitely many solutions

If the solution is: 0=1

No solution