Answer:
See steps below on how to obtain the final solution
[tex]x=2\\y=0[/tex]
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:
[tex]5x-y=10\\-3x+4y=-6[/tex]
Now let's scale the first equation by dividing it by 5 (the leading coefficient for x):
[tex]x-\frac{1}{5} y=2\\-3x+4y=-6[/tex]
now multiply row 1 by 3 and combine with row 2 :
[tex]3\,x-\frac{3}{5} y=6\\-3x+4y=-6\\ \\0+\frac{17}{5} y=0[/tex]
now replace the second row by this combination:
[tex]x-\frac{1}{5} y=2\\0+\frac{17}{5} y=0[/tex]
Now multiply the second row by 5/17:
[tex]x-\frac{1}{5} y=2\\0+} y=0[/tex]
multiply the bottom row by 1/5 and combine with the first row to eliminate the term in y:
[tex]x-\frac{1}{5} y=2\\0+\frac{1}{5} y=0\\ \\x-0=2[/tex]
Now we have the answer to the system:
[tex]x=2\\y=0[/tex]
