Question

{2.x+3.y=6
{5.x+12.y=15

Tira uma duvida como que responde

Answer 1

    $\left \{{{2x+3y=6} \atop {5x+12y=15}} \right.$ ⇔

⇔ $\left \{{{2x=6-3y} \atop {12y=15-5x}} \right.$ ⇔

⇔ $\left \{{{x=\frac{6-3y}{2}} \atop {y=\frac{15-5x}{12}}} \right.$ ⇔

⇔ $\left \{{{x=\frac{6-3y}{2}} \atop {y=\frac{15-5*(\frac{6-3y}{2})}{12}}} \right.$ ⇔

⇔ $\left \{{{x=\frac{6-3y}{2}} \atop {y=\frac{\frac{30}{2} -(\frac{30-15y}{2})}{12}}} \right.$ ⇔

⇔ $\left \{{{x=\frac{6-3y}{2}} \atop {y=\frac{30-(30-15y)}{12*2}}} \right.$ ⇔

⇔ $\left \{{{x=\frac{6-3y}{2}} \atop {y=\frac{30-30+15y}{24}}} \right.$ ⇔

⇔ $\left \{{{x=\frac{6-3y}{2}} \atop {y=\frac{15y}{24}}} \right.$ ⇔

⇔ $\left \{{{x=\frac{6-3y}{2}} \atop {\frac{24y}{24} =\frac{15y}{24}}} \right.$ ⇔

⇔ $\left \{{{x=\frac{6-3y}{2}} \atop {24y=15y}} \right.$ ⇔

⇔ $\left \{{{x=\frac{6-3y}{2}} \atop {24y-15y=0}} \right.$ ⇔

⇔ $\left \{{{x=\frac{6-3y}{2}} \atop {9y=0}} \right.$ ⇔

⇔ $\left \{{{x=\frac{6-3*0}{2}} \atop {y=0}} \right.$ ⇔

⇔ $\left \{{{x=\frac{6}{2}} \atop {y=0}} \right.$ ⇔

⇔ $\left \{{x=3} \atop {y=0}} \right.$

                                            (x ; y) = (3 ; 0)