Question

How do you solve using gaussian elimination or gauss Jordan elimination, 3x – 10y = -25 , 4x + 40y = 20 ?

Answer 1

In the gaussian elimination method, we form a matrix and all the inputs of the matrix are the coefficients and constants of the linear equation. First row of the matrix is formed by coefficients and constants of the first equation, second for the second equation and this goes on. So the first row of the matrix will be 3, – 10, -25 and the second row is 4, 40, 20. Then we perform row operations to solve the equations.

Complete step by step solution:
Equations given in the question is 3x – 10y = -25 and 4x + 40y = 20 , if we write in matrix form we get
$\left| \begin{matrix} 3 & -10 & -25 \\\ 4 & 40 & 20 \\\ \end{matrix} \right|$
Now we can perform row operation ${{R}_{2}}$, let’s multiply 4 with ${{R}_{1}}$ then add it to ${{R}_{2}}$
$\left| \begin{matrix} 3 & -10 & -25 \\\ 16 & 0 & -80 \\\ \end{matrix} \right|$
Now we can say 16x is equal to -80, so x is equal to -5
If we put x equal to -5 in 3x – 10y = -25 we get -15 – 10y = -25 so x is equal to 1

So, x = -5 and y = 1 are solutions of the system of equations.

Note: We can check whether our answer is correct or not by putting x and y value in the equation. if one of them does not satisfy, then our answer is incorrect. So, by putting x = -5 and y = 1 in the equation 3x – 10y = -25 we get -15 – 10 = -25 which is correct. Now if we put x = -5 and y = 1 in, 4x + 40y = 20 we get – 20 + 40 = 20 which is correct. So, our answer is correct.