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skelet666 [1.2K]
3 years ago
14

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

Mathematics
1 answer:
scoray [572]3 years ago
7 0

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

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T(1,4)  ;   A(4,4)  ;   P(3,0)

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Answer:

(0,1)

Step-by-step explanation:

There is a solution where the two equations intersect, therefore:

3x+1=2x+1

3x-2x=1-1

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If we plug this 0 value into the x of both equations, we get a y value of 1:

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OR

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Therefore, there is a solution at (0,1)

<em>I hope this helped! :)</em>

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