1) [tex]\left \{ {{y-x=1} \atop {5x+y=6}} \right.[/tex]
[tex]\left \{ {{y=1+x} \atop {5x+y=6}} \right. \\5x+1+x=6\\x=\frac{5}{6}\\y=1+\frac{5}{6}=\frac{11}{6}[/tex]
2)[tex]\left \{ {{x-\sqrt{2}y=0} \atop {\sqrt{2}x+y=1}} \right.[/tex]
[tex]\left \{ {{x-\sqrt{2}y=0 } \atop {2x+\sqrt{2} y=\sqrt{2} }} \right. \\3x=\sqrt{2} \\x=\frac{\sqrt{2} }{3} \\\frac{\sqrt{2} }{3} -\sqrt{2} y=0\\y=\frac{1}{3}[/tex]
3) [tex]\left \{ {{10x-7y=-18} \atop {-4x+5y=16 => x=-4+\frac{5}{4}y }} \right. \\10(-4+\frac{5}{4}y)-7y=-18\\ y=4\\x=-4+5\\x=1[/tex]
4) [tex]\left \{ {{5x-4y=-23} \atop {7x+6y=-9}} \right. \\\left \{ {{15x-12y=-69} \atop {14x+12y==-18}} \right. \\29x=-87\\x=-3\\7(-3)+6y=-9\\y=2[/tex]
