Solve the system of linear equations using Gaussian elimination with back-substitution.
-10x - 7y = 3
-7x + 6y = 13
A) (1, -1)
B) (-1, 1)
C) (-10, 10)
D) (10, -10)

Question

Quizplus · Accepted Answer

The solution to the system of equations is found by first using Gaussian elimination to reduce the system to upper triangular form, and then applying back-substitution. 1. Multiply the first equation by 7 and the second by 10 to eliminate x:   -70x - 49y = 21   -70x + 60y = 1302. Subtract the first new equation from the second to eliminate x:   109y = 1093. Solve for y:   y = 109 / 109 = 14. Substitute y = 1 into one of the original equations to solve for x:   -10x - 7(1) = 3   -10x - 7 = 3   -10x = 10   x = -1Therefore, the solution is x = -1, y = 1, which corresponds to choice B.

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