Answer: x = 5, y = 2
Explanation:
To solve the system of linear equations using the elimination method, we'll eliminate one variable by adding the two equations together. Let's start:
Original equations:
-5x + 3y = -19
-x - 3y = -11
Adding the two equations eliminates the variable "y":
(-5x + 3y) + (-x - 3y) = -19 + (-11)
-5x + 3y - x - 3y = -19 - 11
-6x = -30
Dividing both sides of the equation by -6:
-6x / -6 = -30 / -6
x = 5
Now that we have the value of x, we can substitute it back into one of the original equations to find y. Let's use the second equation:
-x - 3y = -11
-5 - 3y = -11
Simplifying the equation:
-3y = -11 + 5
-3y = -6
Dividing both sides of the equation by -3:
-3y / -3 = -6 / -3
y = 2
Therefore, the solution to the system of equations is x = 5 and y = 2.