Question

Use gauss-jordan elimination to solve the following linear system: -3x + 4y = -6 5x - y = 10

Answer 1

Answer:

See steps below on how to obtain the final solution

$x=2\\y=0$

using Gauss elimination

Step-by-step explanation:

Let's write this system with the equations swapped since we want the largest value for the x dependence in the top row:

$5x-y=10\\-3x+4y=-6$

Now let's scale the first equation by dividing it by 5 (the leading coefficient for x):

$x-\frac{1}{5} y=2\\-3x+4y=-6$

now multiply row 1 by 3 and combine with row 2 :

$3\,x-\frac{3}{5} y=6\\-3x+4y=-6\\ \\0+\frac{17}{5} y=0$

now replace the second row by this combination:

$x-\frac{1}{5} y=2\\0+\frac{17}{5} y=0$

Now multiply the second row by 5/17:

$x-\frac{1}{5} y=2\\0+} y=0$

multiply the bottom row by 1/5 and combine with the first row to eliminate the term in y:

$x-\frac{1}{5} y=2\\0+\frac{1}{5} y=0\\ \\x-0=2$

Now we have the answer to the system:

$x=2\\y=0$