Use substitution to find the solution to 3x-y=-2 , -9x+3y=6?

Question

a. no solutions

b. (2,8)

c. any x such that y=3x+2

Answer 1

the work:

solve for y in equation 2

     y=6+9x

place in equation 1 (substitution)

    3x-(6+9x)=-2

distribute the negative

    3x-6-9x=-2

solve for x

    -6x=4     x=-2/3

solve for y

     y=6+9(-2/3)  y=0

check in first equation

     3(-2/3)-(0)=-2    -2 equals -2

since the answers we found (-2/3,0) work. the answer is c. any x such that y=3x=2 because (2,8) works too and

y+2+3x

-9x+3(2+3x)=6

-9x+6+9x=6

this leaves 6=6

when a number equals itself this always means that there are infinite solutions in the problem you are solving.

Answer 2

y=2+3x

-9x+3(2+3x)=6

-9x+6+9x=6

6=6

The answer would be C.

Answer 3

3x-y= -2

-9x+3y= 6

3x-y= -2

-y= -3x-2 ---Subtract 3x from both sides.

y= 3x+2 ---Divide both sides by -1.

-9x+3y= 6

-9x+3(3x+2)= 6 ---Substitute 3x+2 for y.

-9x+9x+6= 6 ---Distribute 3 to (3x+2).

6= 6 ---Simplify.

C.

Answer 4

answer: (2,8)

reason:

plug in (2,8) for x and y respectively

3x-y= -2

3(2)-8= -2

6-8= -2

that checks!!!

-9x=3y=6

-9(2)+3(8)=6

-18+24=6

that checks too!!!

so the right answer is: (2,8)