Question

-6x+2y=-14. -9x+3y=-21

Answer 1

If you divide first equation by two and the second by three they are both the same line so there are infinitely many solutions.

Answer 2

Answer:

-no solution-

Step-by-step explanation:

Let's solve your system by elimination.

−6x+2y=−14;−9x+3y=−21

Multiply the first equation by 3,and multiply the second equation by -2.

3(−6x+2y=−14)

−2(−9x+3y=−21)

Becomes:

−18x+6y=−42

18x−6y=42

Add these equations to eliminate y:

0=0

Answer:

Infinitely many solutions.

Let's solve your system by substitution.

−6x+2y=−14;−9x+3y=−21

Step: Solve−6x+2y=−14for x:

−6x+2y=−14

−6x+2y+−2y=−14+−2y(Add -2y to both sides)

−6x=−2y−14

−6x

−6

=

−2y−14

−6

(Divide both sides by -6)

x=

1

3

y+

7

3

Step: Substitute

1

3

y+

7

3

forxin−9x+3y=−21:

−9x+3y=−21

−9(

1

3

y+

7

3

)+3y=−21

−21=−21(Simplify both sides of the equation)

−21+21=−21+21(Add 21 to both sides)

0=0

Answer:

Infinitely many solutions.