Solve the system of linear equations using Gauss-Jordon elimination with back-substitution.
-9x - 6y = 6
-7x + 6y = 26
A) (2, -2)
B) (-2, 2)
C) (-9, 12)
D) (12, -9)

Question

Quizplus · Accepted Answer

The correct solution is (-2, 2). By applying Gauss-Jordan elimination, we first aim to transform the system of equations into reduced row echelon form (RREF). Starting with the system:1. -9x - 6y = 62. -7x + 6y = 26We can multiply the first equation by 1 to make the leading coefficient -9, and the second equation by 1 to keep the coefficients as they are. This doesn't change the system but prepares us for elimination steps.Next, to eliminate y from the second equation, we can add the two equations together because -6y + 6y = 0. Before doing that, it's more straightforward to first make the coefficients of y the same in absolute value, which they already are. So, we proceed directly to add the equations:-9x - 6y + (-7x + 6y) = 6 + 26-16x = 32Solving for x gives x = -2.To find y, we substitute x = -2 into one of the original equations. Using the first equation:-9(-2) - 6y = 618 - 6y = 6-6y = -12y = 2Therefore, the solution to the system of equations is x = -2, y = 2, which corresponds to choice B.

Solve the System of Linear Equations Using Gauss-Jordon Elimination with Back-Substitution