Gaussian elimination method

Question

{2x-3y=13, 3x-4y=18 Solve in Gaussian elimination method

Answer 1

Greetings! Lets solve this shall we ?

So, we must solve this system of linear equations via Gaussian Elimination using elementary row operations such that

2x - 3y = 13

3x - 4y = 18........We first apply R₂ - R₁ --> R₁ to change R₁ such that

x - y = 5

3x - 4y = 18.............Then we apply 4*R₁ - R₂ --> R₂ to change R₂ such that

x - y = 5

x + 0 = 2.............Then x = 2. Finally, we substitute x = 2 into x - y = 5 to get

2 - y = 5

-y = 3

y = -3

I hope this helped!

Answer 2

2x - 3y = 13

3x - 4y = 18

eliminate the variable x:

(-3/2)*(2x - 3y = 13) is -3x + (9/2) y = -39/2

Add this to the other equation:

3x - 4y = 18

-3x +(9/2)y = -39/2

0 + (17/2)y = (-3/2)

y = (-3/2)*(2/17)

y = -3/17 = 0.1765

3x - 4(-3/17) = 18

3x + 12/17 = 18

3x = 17 + 17/17 - 12/17

3x = 17 + 5/17

x = 17.2941

x = 17.2941 and y = 0.1765 is the answer that you seek.

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