Algebra 2 problem

Question

The system of equations:

 

2x+2y-z=13

4x-y=7

7y-4y=11

 

represents the number of red, green, and blue cubes you will need to help your younger sister practice her addition and subtraction. Use x as the number of red cubes, y as the number of green cubes, and z as the number of blue cubes. What is the number of each color of cubes you will need to gather to help your sister?

 

A) 3 red, 5 green, and 3 blue

 

B) 4 red, 9 green, and 13 blue

Answer 1

 

2x+2y-z=13

4x-y=7

7y-4z=11

from eq1     2x+2y-13=z

substitute into eq3

7y-4(2x+2y-13)=11

7y-8x-8y+52=11

-y-8x=11-52

-y-8x=-41

y+8x=41 and now use this with eq2

-y+4x=7

add

12x=48

x=4

you're basically done because the answer is B, but let's continue

eq2 4*4-y=7

16-y=7

16-7=y

y=9

substitute into either eq1 or eq3

7*9-4z=11

63-4z=11

-4z=11-63

-4z=-52

4z=52

z=13

4, 9, and 13