a)
[tex]\left \{ {{x-2y=-2} \atop {3x-5y=-3}} \right.[/tex]
[tex]\left \{ {{x=-2+2y} \atop {3x-5y=-3}} \right.[/tex]
3(-2+2y) -5y = -3
y=3
x = - 2 + 2 * 3
x = 4
(x,y) = (4,3)
[tex]\left \{ {{4-2*3=-2} \atop {3*4-5*3=-3}} \right.[/tex]
[tex]\left \{ {{-2=-2} \atop {-3=-3}} \right.[/tex]
(x,y) = (4,3)
b)
[tex]\left \{ {{5x+4y=-6} \atop {2x+y=-3}} \right.[/tex]
[tex]\left \{ {{5x+4y=-6} \atop {y=-3-2x}} \right.[/tex]
5x+4(-3-2x)= -6
x= -2
y= -3 - 2 * (-2)
y=1
(x,y) = (-2,1)
[tex]\left \{ {{5*(-2)+4*1= -6} \atop {2x (-2) + 1= -3}} \right.[/tex]
[tex]\left \{ {{-6 = -6} \atop {-3 = -3}} \right.[/tex]
(x,y) = (-2,1)
c)
[tex]\left \{ {{6x - y = 7} \atop {-3x + 2y = 4}} \right.[/tex]
[tex]\left \{ {{y= -7 + 6x} \atop {-3x + 2y = 4}} \right.[/tex]
-3x + 2(-7 +6x) = 4
x = 2
y = -7 + 6 * 2
y = 5
(x,y) = (2,5)
[tex]\left \{ {{6*2 - 5 = 7\\} \atop {-3 * 2 + 2*5 =4}} \right.[/tex]
[tex]\left \{ {{7=7} \atop {4=4}} \right.[/tex]
(x,y) = (2,5)
