Відповідь:

1.x=1,y=2

3.x=4,y=2

5.a=[tex]\frac{3}{2}[/tex],b=[tex]\frac{1}{2}[/tex]

Пояснення:

1. [tex]\left \{ {{5x+y=7} \atop {7x-4y=-1}} \right.[/tex]  [tex]\left \{ {{y=7-5x} \atop {7x-4(7-5x)=-1}} \right.[/tex]

  [tex]7x-28+20x=-1\\27x=27\\x=1\\y=7-5*1\\y=2[/tex]

3.[tex]\left \{ {{5x-2y=16} \atop {8x+3y=38}} \right.[/tex]   [tex]\left \{ {{x=\frac{2y+16}{5} } \atop {8(\frac{2y+16}{5} })+3y=38} \right.[/tex]

   [tex]8(\frac{2y}{5}+\frac{16}{5})+3y=38\\ \frac{16y}{5}+\frac{128}{5} +3y=38\\ \frac{16y+128+15y}{5}=\frac{190}{5} \\ 16y+128+15y=190\\31y=62\\y=2\\5x-4=16\\5x=20\\x=4[/tex]

5.[tex]\left \{ {{4a+6b=9} \atop {3a-5b=2}} \right.[/tex]  [tex]\left \{ {{a=\frac{9-6b}{4} } \atop {3(\frac{9-6b}{4} )-5b=2}} \right.[/tex]

   [tex]3(\frac{9-6b}{4} )-5b=2\\3(\frac{9}{4}-\frac{6b}{4})-5b=2\\ \frac{27}{4}-\frac{18b}{4}-5b=2\\- \frac{38b}{4}=-\frac{19}{4}\\ b=\frac{19}{38}=\frac{1}{2}\\ a=\frac{9-3}{4} =\frac{3}{2}[/tex]