Question

determine a solução do sistema linear ?

 

4 x - y = 1

2 x + 3 y = 2

Answer 1

$\left\{\begin{matrix} 4x-y=1 & \rightarrow y = 4x-1 \\ 2x+3y=2 & \end{matrix}\right. \\\\ \rightarrow 2x+3y=2 \\\\ 2x+3(4x-1) = 2 \\\\ 2x+12x-3 = 2 \\\\ 14x = 5 \\\\ x= \boxed{\frac{5}{14}} \\\\\\ \text{voltando no} \ y \\\\ y = 4x-1 \\\\ y = 4 \cdot \frac{5}{14}-1 \\\\ y = \frac{20}{14}-1 \\\\ y = \frac{20}{14}-\frac{14}{14} \\\\ y = \frac{6^{\div2}}{14^{\div 2}} = \boxed{\frac{3}{7}}$


Portanto, a solução:

$\boxed{\boxed{S = \{\frac{5}{14},\frac{3}{7}\}}}$