Answer:
x = -3 and y = 1.
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.