Question

What is the value of A, B, C and D?

7=A+C
-1=B+D
17=A+3C
-3=B+3D

Answer 1

`color(red)(=>"A"=2; "B"=0; "C"=5 and "D"=-1`

Explanation:

The 4 equations we have are:-

1st equation: `color(blue)(7="A"+"C"`

2nd equation: `color(darkorange)(-1="B"+"D"`

3rd equation:`color(green)(17="A"+3"C"`

4th equation: `color(magenta)(-3="B"+3"D"`

Taking the first and third equations first and solving for A and C

`color(blue)(=>7="A"+"C"`...… 1st eqn

`=>"A"=7-"C"`

`color(green)(=>17="A" +3"C"`..... 3rd eqn

`=>17=7-"C"+3"C"`

`=>17-7=2"C"`

`=> 10=2"C"`

`color(red)("C"=5 and "A" = 7-"C"=2`

Taking the 2nd and 4th equations first and solving for A and C.

`color(darkorange)(=>-1="B"+"D"`.... 2nd eqn

`=> "B"=-1-"D"`

`color(magenta)(=>-3="B"+3"D"`...4th eqn

`=>-3=-1-"D"+3"D"`

`=>-3+1=-"D"+3"D"`

`=>-2=2"D"`

`color(red)(=>"D"=-1 and "B"=-1-"D"=0`

~Hope this helps! :)

Answer 2

`A=2,B=0,C=5,D=-1`

Explanation:

Multiplying the first equation by `-1` and adding to the third we get

`2C=10` so `C=5`
From here we get `A=2`

Multiplying the second by `-1` and adding to the last one
`D=-1`
so
`B=0`

Answer 3

`A=2`, `B=0`, `C=5` and `D=-1`

Explanation:

As `7=A+C` and `17=A+3C`, subtracting former from latter we get

`10=2C` or `C=10/2=5`

and as `A+C=7`, `A=7-5=2`

Similarly as `-1=B+D` and `-3=B+3D`, subtracting former from latter we get

`-3-(-1)=2D` or `2D=-3+1=-2` and `D=-1`

And as `B+D=-1`, `B=-1-(-1)=-1+1=0`