Question

Can someone help me with these?

Answer 1

QUESTION 12

The given equations are;

$-6x+3y=33...(1)$ and $-4x+y=14...(2)$

Make y the subject in equation (2).

$y=4x+16..(3)$

We put this equation (3) into equation (1) to get;

$-6x+3(4x+16)=33$

Expand;

$-6x+12x+48=33$

$6x=33-48$

$6x=-15$

$x=-\frac{5}{2}$

Put $x=-\frac{5}{2}$ into equation (3)

$y=4(\frac{-5}{2})+16$

$y=-10+16=6$

$x=-\frac{5}{2},y=6$

QUESTION 12

The given equations are

$2y=5x-1...(1)$

and

$x+y=-1...(2)$

Make y the subject in equation (2)

$y=-x-1...(3)$

Put equation (3) into (1)

$2(-x-1)=5x-1$

$-2x-2=5x-1$

$-2+1=5x+2x$

$7x=-1$

$x=-\frac{1}{7}$

Put $x=-\frac{1}{7}$ into equation (3).

$y=--\frac{1}{7}-1=-\frac{6}{7}$

QUESTION 13

The given equations are

$x+y+z=-1...(1)$

$2x+4y+z=1...(2)$

$x+2y-3z=-3...(3)$

Make x the subject in equation (3).

$x=3z-2y-3...(4)$

Put equation (4) into equation (1)

$3z-2y-3+y+z=-1$

$4z-y=2...(5)$

Put equation (4) into equation (2)

$2(3z-2y-3)+4y+z=1$

$6z-4y-6+4y+z=1$

$7z=7$

$z=1$

Put z=1 in equation (5)

$4(1)-y=2$

$y=4-2$

$y=2$

Put y=2 and z=1 into equation(4)

$x=3(1)-2(2)-3$

$x=-4$