Question

Solve the system of equations using Gaussian elimination:

x - 3y = 3
-11x - 2y = 2
A) x = -1, y = 2
B) x = -2, y = -1
C) x = 1, y = 0
D) x = 2, y = -2

Answer 1

To solve the system of equations using Gaussian elimination, multiply one equation by a coefficient to eliminate one variable, then add the equations together to solve for the remaining variable.

Step-by-step explanation:

To solve the system of equations using Gaussian elimination, you need to eliminate one of the variables by multiplying one of the equations by a appropriate coefficient and then adding the equations together.

In this case, we can multiply the first equation by 11 and the second equation by -1 to eliminate the x variable. This gives us:

11x - 33y = 33

11x + 2y = -2

Now, add the two equations together:

-31y = 31

Divide both sides of the equation by -31 to solve for y:

y = -1

Substitute this value of y back into one of the original equations to solve for x:

x - 3(-1) = 3

x + 3 = 3

x = 0

Therefore, the solution to the system of equations is x = 0 and y = -1.