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Consider the system of linear equations: $$ \begin{align*} 2x + 3y &= 5 \\ 4x - y &= 2 \end{align*} $$

I'm trying to find the solutions for x and y. If anyone could provide insights or a step-by-step solution, I would greatly appreciate it.

I need to solve it by Cramer's method, I have used Gaussian elimination and I have made graphs and the solution must be x=0.79, y=1.14

EDIT: my attempt $$ \Delta = \begin{vmatrix} 2 & 3 \\ 4 & -1 \end{vmatrix} = (2 \cdot -1) - (4 \cdot 3) = -14 $$

For $ \Delta_x $ and $ \Delta_y $, I substituted the constants:

$$ \Delta_x = \begin{vmatrix} 5 & 3 \\ 2 & -1 \end{vmatrix} = (5 \cdot -1) - (2 \cdot 3) = -11 $$

$$ \Delta_y = \begin{vmatrix} 2 & 5 \\ 4 & 2 \end{vmatrix} = (2 \cdot 2) - (4 \cdot 5) = -18 $$

Now

$$ x = \frac{\Delta_x}{\Delta} = \frac{-11}{-14} \quad \text{(correct)} $$

$$ y = \frac{\Delta_y}{\Delta} = \frac{-18}{-14} \quad \text{(incorrect)} $$

Dalit Eli
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1 Answers1

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$$ \Delta_y = \begin{vmatrix} 2 & 5 \\ 4 & 2 \end{vmatrix} = (2 \cdot 2) - (4 \cdot 5) =4-20= -16 $$ Then,

$y=16/14=1.14$ approximately

bladee
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