Question

Rezolvati urmatoarele sisteme de ecuatii :

a) 2x -y=17
y=3

b)3x-4y=2
y=x+1

c)-x+3y=11
x=-2

d) -4x +5y=17
x-y=2

Answer 1

$\left \{ {{2x-y=17} \atop {y=3}} \right. \\ \left \{ {{2x-3=17} \atop {y=3}} \right. \\ \left \{ {{2x=17+3} \atop {y=3}} \right. \\ \left \{ {{2x=20} \atop {y=3}} \right. \\ \left \{ {{x=10} \atop {y=3}} \right.$

$\left \{ {{3x-4y=2} \atop {y=x+1}} \right. \\ \left \{ {{3x-4(x+1)=2} \atop {y=x+1}} \right. \\ \left \{ {{3x-4x-4=2} \atop {y=x+1}} \right. \\ \left \{ {{-x-4=2} \atop {y=x+1}} \right. \\ \left \{ {{-x=6|(-1)} \atop {y=x+1}} \right. \\ \left \{ {{x=-6} \atop {y=x+1}} \right. \\ \left \{ {{x=-6} \atop {y=-6+1}} \\ \left \{ {{x=-6} \atop {y=-5}} \right. \right.$

$\left \{ {{-x+3y=11} \atop {x=-2}} \right. \\ \left \{ {{2+3y=11} \atop {x=-2}} \right. \\ \left \{ {{3y=11-2} \atop {x=-2}} \right. \\ \left \{ {{3y=9} \atop {x=-2}} \right. \\ \left \{ {{y=3} \atop {x=-2}} \right.$

$\left \{ {{-4x+5y=17} \atop {x-y=2}} \right. \\ \left \{ {{-4x+5y=17} \atop {x=2+y}} \right. \\ \left \{ {{-4(2+y)+5y=17} \atop {x=2+y}} \right. \\ \left \{ {{-8-4y+5y=17} \atop {x=2+y}} \right. \\ \left \{ {{-8+y=17} \atop {x=2+y}} \right. \\ \left \{ {{y=17+8} \atop {x=2+y}} \right. \\ \left \{ {{y=25} \atop {x=2+y}} \right. \\ \left \{ {{y=25} \atop {x-25=2}} \right. \\ \left \{ {{y=25} \atop {x=2+25}} \right. \\ \left \{ {{y=25} \atop {x=27}} \right.$