QUESTION 12
The given equations are;
[tex]-6x+3y=33...(1)[/tex] and [tex]-4x+y=14...(2)[/tex]
Make y the subject in equation (2).
[tex]y=4x+16..(3)[/tex]
We put this equation (3) into equation (1) to get;
[tex]-6x+3(4x+16)=33[/tex]
Expand;
[tex]-6x+12x+48=33[/tex]
[tex]6x=33-48[/tex]
[tex]6x=-15[/tex]
[tex]x=-\frac{5}{2}[/tex]
Put [tex]x=-\frac{5}{2}[/tex] into equation (3)
[tex]y=4(\frac{-5}{2})+16[/tex]
[tex]y=-10+16=6[/tex]
[tex]x=-\frac{5}{2},y=6[/tex]
QUESTION 12
The given equations are
[tex]2y=5x-1...(1)[/tex]
and
[tex]x+y=-1...(2)[/tex]
Make y the subject in equation (2)
[tex]y=-x-1...(3)[/tex]
Put equation (3) into (1)
[tex]2(-x-1)=5x-1[/tex]
[tex]-2x-2=5x-1[/tex]
[tex]-2+1=5x+2x[/tex]
[tex]7x=-1[/tex]
[tex]x=-\frac{1}{7}[/tex]
Put [tex]x=-\frac{1}{7}[/tex] into equation (3).
[tex]y=--\frac{1}{7}-1=-\frac{6}{7}[/tex]
QUESTION 13
The given equations are
[tex]x+y+z=-1...(1)[/tex]
[tex]2x+4y+z=1...(2)[/tex]
[tex]x+2y-3z=-3...(3)[/tex]
Make x the subject in equation (3).
[tex]x=3z-2y-3...(4)[/tex]
Put equation (4) into equation (1)
[tex]3z-2y-3+y+z=-1[/tex]
[tex]4z-y=2...(5)[/tex]
Put equation (4) into equation (2)
[tex]2(3z-2y-3)+4y+z=1[/tex]
[tex]6z-4y-6+4y+z=1[/tex]
[tex]7z=7[/tex]
[tex]z=1[/tex]
Put z=1 in equation (5)
[tex]4(1)-y=2[/tex]
[tex]y=4-2[/tex]
[tex]y=2[/tex]
Put y=2 and z=1 into equation(4)
[tex]x=3(1)-2(2)-3[/tex]
[tex]x=-4[/tex]
