Question

Can someone help me with these?

Solve each system of equations. Check each answer algebraically.
11. -­6x + 3y = 33
-­4x + y = 16
12. 2y = 5x ­-1
x + y = -­1
13. x + y + z = -­1
2x + 4y + z = 1
x + 2y ­- 3z = ­-3

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=-(5)/(2)`

Put
`x=-(5)/(2)` into equation (3)

`y=4((-5)/(2))+16`

`y=-10+16=6`

`x=-(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=-(1)/(7)`

Put
`x=-(1)/(7)` into equation (3).

`y=--(1)/(7)-1=-(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`