Question

resolva os sistemas pelo método da adição:​

Answer 1

Pergunta 13.

a) $\left \{ {{3x+5y=11} \atop {2x-y=16}} \right.\left \{ {{3x+5y=11} \atop {2x-16=y}} \right.\left \{ {{3x+(2x-16)=11} \atop {2x-16=y}} \right.\left \{ {{5x=27} \atop {2x-16=y}} \right.\left \{ {{x=\frac{5}{27} } \atop {2(\frac{5}{27})-16=y }} \right.\left \{ {{x=\frac{5}{27}} \atop {y=-\frac{422}{27} }} \right.$

b) $\left \{ {{x+y=8} \atop {x-2y=2}} \right. \left \{ {{x=8-y} \atop {8-y-2y=2}} \right. \left \{ {{x=8-y} \atop {6=3y}} \right. \left \{ {{x=8-y} \atop {y=2}} \right. \left \{ {{x=8-2} \atop {y=2}} \right. \left \{ {{x=6} \atop {y=2}} \right.$

c) $\left \{ {{3x+3y=21} \atop {2x-y=5}} \right. \left \{ {{3x+3y=21} \atop {2x-5=y}} \right. \left \{ {{3x+3(2x-5)=21} \atop {2x-5=y}} \right. \left \{ {{3x+6x-15=21} \atop {2x-5=y}} \right. \left \{ {{9x=36} \atop {2x-5=y}} \right. \left \{ {{x=4} \atop {2x-5=y}} \right. \left \{ {{x=4} \atop {2*4-5=y}} \right.\left \{ {{x=4} \atop {y=3}} \right.$

d) $\left \{ {{x+y=2} \atop {4x-2y=5}} \right. \left \{ {{x=2-y} \atop {4(2-y)-2y=5}} \right. \left \{ {{x=2-y} \atop {8-4y-2y=5}} \right. \left \{ {{x=2-y} \atop {3=6y}} \right. \left \{ {{x=2-y} \atop {y=\frac{1}{3} }} \right.\left \{ {{x=2-\frac{1}{3} } \atop {y=\frac{1}{3}}} \right. \left \{ {{x=\frac{5}{3} } \atop {y=\frac{1}{3}}} \right.$

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

f) $\left \{ {{5x-y=4} \atop {2x-y=-5}} \right. \left \{ {{y=5x-4} \atop {2x-5x-4=-5}} \right. \left \{ {{y=5x-4} \atop {3x=1}} \right. \left \{ {{y=5*\frac{1}{3}-4 } \atop {x=\frac{1}{3} }} \right. \left \{ {{y=-\frac{7}{3} } \atop {x=\frac{1}{3} }} \right.$

Pergunta 14.

a) $\left \{ {{3x+2y=2} \atop {2x+3y=3}} \right.\left \{ {{3x=2-2y} \atop {2x+3y=3}} \right. \left \{ {{x=\frac{2}{3} -\frac{2y}{3} } \atop {2(\frac{2}{3}-\frac{2y}{3})+3y=3  }} \right. \left \{ {{x=\frac{2}{3} -\frac{2y}{3}} \atop {\frac{4}{3} -\frac{4y}{3} +3y=3}} \right. \left \{ {{x=\frac{2}{3} -\frac{2y}{3}} \atop {\frac{5y}{3} =\frac{5}{3} }} \right. \left \{ {{x=\frac{2}{3} -\frac{2*1}{3}} \atop {y=1}} \right. \left \{ {{x=0} \atop {y=1}} \right.$

b) $\left \{ {{4x+2y=-2} \atop {2x+3y=-7}} \right. \left \{ {{4x=-2-2y} \atop {2x+3y=-7}} \right. \left \{ {{x=-\frac{1}{2} -\frac{1y}{2} } \atop {2(-\frac{1}{2} -\frac{1y}{2})+3y=-7}} \right. \left \{ {{x=-\frac{1}{2} -\frac{1y}{2}} \atop {-1-1y+3y=-7}} \right. \left \{ {{x=-\frac{1}{2} -\frac{1y}{2}} \atop {2y=-6}} \right. \left \{ {{x=-\frac{1}{2} -\frac{1y}{2}} \atop {y=-3}} \right. \left \{ {{x=-\frac{1}{2} -\frac{1*(-3)}{2}} \atop {y=-3}} \right.$$\left \{ {{x=-\frac{1}{2}+\frac{3}{2}  } \atop {y=-3}} \right. \left \{ {{x=1} \atop {y=-3}} \right.$

c) $\left \{ {{3x+4y=2} \atop {2x+5y=-1}} \right. \left \{ {{3x=2-4y} \atop {2x+5y=-1}} \right. \left \{ {{x=\frac{2}{3} -\frac{4y}{3} } \atop {2(\frac{2}{3} -\frac{4y}{3})+5y=-1}} \right. \left \{ {{x=\frac{2}{3} -\frac{4y}{3}} \atop {\frac{4}{3} -\frac{8y}{3}+5y=-1}} \right. \left \{ {{x=\frac{2}{3} -\frac{4y}{3} } \atop {\frac{7y}{3} =\frac{5}{3} }} \right. \left \{ {{y=2} \atop {x=2}} \right. \left \{ {{x=\frac{2}{3} -\frac{4y}{3} } \atop {y=\frac{5}{7} }} \right.$$\left \{ {{x=\frac{2}{3}-\frac{4}{3} *\frac{5}{7}  } \atop {y=\frac{5}{7}}} \right. \left \{ {{x=\frac{14}{21} -\frac{20}{21} } \atop {y=\frac{5}{7}}} \right. \left \{ {{x=-\frac{6}{21} } \atop {y=\frac{5}{7}}} \right.$

d) $\left \{ {{3x+5y=11} \atop {4x-3y=5}} \right. \left \{ {{3x=11-5y} \atop {4x-3y=5}} \right. \left \{ {{x=\frac{11}{3} -\frac{5y}{3} } \atop {4(\frac{11}{3} -\frac{5y}{3})-3y=5}} \right.\left \{ {{x=\frac{11}{3} -\frac{5y}{3}} \atop {\frac{44}{3} -\frac{20y}{3}-3y=5 }} \right. \left \{ {{x=\frac{11}{3} -\frac{5y}{3}} \atop {\frac{29y}{3} =-\frac{29}{3} }} \right.\left \{ {{x=\frac{11}{3} -\frac{5y}{3}} \atop {y=-1}} \right. \left \{ {{x=\frac{16}{3} } \atop {y=-1}} \right.$

e) $\left \{ {{5x-3y=9} \atop {4x+2y=16}} \right. \left \{ {{y=-3-\frac{5x}{3} } \atop {4x+2(-3-\frac{5x}{3})=16}} \right. \left \{ {{y=-3-\frac{5x}{3} } \atop {4x-6-\frac{10x}{3} =16}} \right. \left \{ {{y=-3-\frac{5x}{3} } \atop {\frac{2x}{3} =22}} \right. \left \{ {{y=-3-\frac{5x}{3} } \atop {x=33}} \right. \left \{ {{y=-3-55} \atop {x=33}} \right. \left \{ {{y=-58} \atop {x=33}} \right.$

f) $\left \{ {{5x-3y=2} \atop {2x-4y=-2}} \right. \left \{ {{5(-1+2y)-3y=2} \atop {x=-1+2y}} \right. \left \{ {{-5+10y-3y=2} \atop {x=-1+2y}} \right. \left \{ {{7y=7} \atop {x=-1+2y}} \right. \left \{ {{y=1} \atop {x=-1+2*1}} \right. \left \{ {{y=1} \atop {x=1}} \right.$