Answer:
a) The solution of the given system is (x,y) = (-4,1)
b) The solution of the given system is (-6,-4)
Step-by-step explanation:
a) Step 1:-
The given equations are [tex]5 x-y = -21[/tex]........(1)
given second equation is [tex]x+y = -3[/tex]......(2)
adding the equations (1) and (2) and cancelled y terms,we get
[tex]5 x+x=-21-3[/tex]
[tex]6x=-24[/tex]
dividing by '6' on both sides,we get
[tex]x=-4[/tex]
Step 2:-
substituting x =-4 in equation (1) and simplification , we get
[tex]5(-4)-y=-21[/tex]
[tex]y=1[/tex]
The solution of the system is (-4,1)
b) Explanation:-
Step 3:-
The given equations are [tex]\frac{5x}{3} -2 y=-2[/tex].........(3)
and second equation is [tex]-x+y=2[/tex]........(4)
solving the equations (3) and (4)
multiply equation (4) with '2'
[tex]-2 x+2 y =4[/tex] .......................(5)
now adding (3) and (5) equations and simplification , we get
[tex]\frac{5x}{3} -2 x=2[/tex]
taking l.c.m we get [tex]\frac{5 x-6 x}{3} =2[/tex]
[tex]\frac{-x}{3} =2[/tex]
[tex]x=-6[/tex]
Step 4:-
substituting x= -6 in equation (3), we get solution
[tex]\frac{5(-6)}{3} -2 y =-2[/tex]
now simplification we get [tex]y = -4[/tex]
The solution of the given system is (-6,-4)
