Question

Solve the matrix of the following using the Gaussian Method.

1. 3x-5y= -2
2x+4y= 7

Answer 1

Answer on Question#43862 – Math – Linear Algebra

Question:

Solve the matrix of the following using the Gaussian Method

$$\begin{array}{l} 3x - 5y = -2 \\ 2x + 4y = 7 \\ \end{array}$$

Solution.

$$1.\begin{cases} 3x - 5y = -2 \\ 2x + 4y = 7 \\ \end{cases}$$

We write the extended system matrix

$$\left[ \begin{array}{cc} 3 & -5 \\ 2 & 4 \end{array} \right]^{-2} \sim \left[ \begin{array}{cc} 6 & -10 \\ -6 & -12 \end{array} \right]^{-4} \sim \left[ \begin{array}{cc} 0 & -22 \\ 2 & 4 \end{array} \right]^{-25}$$

From first row we get $y = \frac{25}{22}$ and from second row we get $2x + 4 * \frac{25}{22} = 7$ hence $2x = \frac{77}{11} - \frac{50}{11} = \frac{27}{11}$. Thus, $x = \frac{27}{22}$

Answer. $x = \frac{27}{22}, y = \frac{25}{22}$

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