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Question

How many solutions are there to the following system of equations?

3x - 9y = 0

-x + 3y = -3

A. 0

B. 1

C. 2

D. Infinitely Many

Answer 1

Favorite Answer

Well first you've got to solve for X and Y by solving first for X in the first equation then putting it in for X in the second equation.

3x - 9y = 0

3x = 9y

x = 3y

-x + 3y = -3

-(3y) + 3y = 3

-3y + 3y = 0

0y=0

And that looks like it sucks so let's start the other way with Y.

-x + 3y = -3

3y = -3 + x

y = -1 + 1/3x

3x - 9y = 0

3x - 9 (-1 + 1/3x) = 0

3x + 9 -3x = 0

9 = 0

And that doesn't make sense either.

I choose A.

Source(s): math genius

Answer 2

3x-9y=0_-x+3y=-3

Since 3y does not contain the variable to solve for, move it to the right-hand side of the equation by subtracting 3y from both sides.

3x-9y=0_-x=-3y-3

Multiply each term in the equation by -1.

3x-9y=0_-x*-1=-3y*-1-3*-1

Multiply -x by -1 to get x.

3x-9y=0_x=-3y*-1-3*-1

Simplify the right-hand side of the equation by multiplying out all the terms.

3x-9y=0_x=3y+3

Replace all occurrences of x with the solution found by solving the last equation for x. In this case, the value substituted is 3y+3.

3(3y+3)-9y=0_x=3y+3

Multiply 3 by each term inside the parentheses.

9y+9-9y=0_x=3y+3

Since 9y and -9y are like terms, add -9y to 9y to get 0.

0+9=0_x=3y+3

Remove the 0 from the polynomial; adding or subtracting 0 does not change the value of the expression.

9=0_x=3y+3

Since 9$0, there are no solutions.

No Solution

Answer is "A"

Answer 3

Keep the first equation as it is, but multiply the second equation by -3 and we get two equations

3x - 9y = 0

3x - 9y = 9

Since the left sides are identical but the right sides are not, there are no possible solutions to these simultaneous equations.