a) [tex]\left \{ {{2x-y=80} \atop {5x-y=70}} \right. \left \{ {{y=-80+2x} \atop {5x-2y=70}} \right.[/tex]
5x-2(-80+2x) = 70
5x+160-4x = 70
x = -90
y = -80+2*(-90)
y = -260
[tex]\left \{ {{2*(-90)-(-260)=80} \atop {5*(-90)-2*(-260)=70}} \right. \left \{ {{80=80} \atop {70=70}} \right.[/tex]
b) [tex]\left \{ {{3x+y-10=0} \atop {2x-y-12=0}} \right. \left \{ {{y=-3x+10} \atop {2x-y-12=0}} \right.[/tex]
2x-(-3x+10)-12 = 0
x = [tex]\frac{22}{5}[/tex]
y = -3*[tex]\frac{22}{5}[/tex]+10
y = [tex]-\frac{16}{5}[/tex]
[tex]\left \{ {{3*\frac{22}{5}+(-\frac{16}{5})-10=0 ) } \atop {2*\frac{22}{5}-(-\frac{16}{5})-12=0 ) }} \right. \left \{ {{0=0} \atop {0=0}} \right.[/tex]
c) [tex]\left \{ {{2x-5y=2} \atop {2x+5y=2}} \right. \left \{ {{2x-5y=2} \atop {2x=2-5y}} \right.[/tex]
2-5y-5y = 2
y = 0
2x = 2-5*0
x = 1
[tex]\left \{ {{2*1-5*0=2} \atop {2*1+5*0=2}} \right. \left \{ {{2=2} \atop {2=2}} \right.[/tex]
d) [tex]\left \{ {{-\frac{1}{3}x+y=3 } \atop {x+y=2}} \right. \left \{ {{y=3+\frac{1}{3}x} \atop {x+y=2}} \right.[/tex]
x+3+[tex]\frac{1}{3}[/tex]x = 2
x = [tex]-\frac{3}{4}[/tex]
y = 3+[tex]\frac{1}{3}[/tex]*([tex]-\frac{3}{4}[/tex])
y = [tex]\frac{11}{4}[/tex]
[tex]\left \{ {{-\frac{1}{3}*(-\frac{3}{4})+\frac{11}{4}=3 } \atop {-\frac{3}{4}+\frac{11}{4}=2 } \right. \left \{ {{3=3} \atop {2=2}} \right.[/tex]
