What is the solution of the system of equations -x+3y=6 and -10x-3y=27?

Answer:
x = -3 and y = 1.

Step-by-step explanation:

The given system of equations is:

-x + 3y = 6 ---(1)

-10x - 3y = 27 ---(2)

To solve this system of equations, we can use the method of elimination or substitution.

Method 1: Elimination

To eliminate the variable y, we can add equations (1) and (2) together:

(-x + 3y) + (-10x - 3y) = 6 + 27

Simplifying the equation gives us:

-11x = 33

Dividing both sides of the equation by -11, we get:

x = -3

Now, we can substitute this value of x into either equation (1) or (2) to find the value of y. Let's use equation (1):

-x + 3y = 6

Substituting x = -3, we have:

-(-3) + 3y = 6

Simplifying the equation gives us:

3 + 3y = 6

Subtracting 3 from both sides of the equation, we get:

3y = 3

Dividing both sides of the equation by 3, we have:

y = 1

Therefore, the solution to the system of equations -x + 3y = 6 and -10x - 3y = 27 is x = -3 and y = 1.

Method 2: Substitution

Let's solve the system of equations using the substitution method.

From equation (1), we can express x in terms of y:

x = 6 - 3y ---(3)

Substitute this expression for x into equation (2):

-10(6 - 3y) - 3y = 27

Simplifying the equation gives us:

-60 + 30y - 3y = 27

Combining like terms, we have:

27y = 87

Dividing both sides of the equation by 27, we get:

y = 3

Now, substitute this value of y into equation (3):

x = 6 - 3(3)

Simplifying the equation gives us:

x = 6 - 9

x = -3

Therefore, the solution to the system of equations -x + 3y = 6 and -10x - 3y = 27 is x = -3 and y = 3.

Both methods lead to the same solution, which is x = -3 and y = 1.