Question

How do you solve the system of equations `3x + 4y = - 14` and `12x - 3y = 20`?

Answer 1

Solution : `x =2/3 , y = -4`

Explanation:

`3x +4y = -14 (1)`

`12x -3y = 20 (2)`

Multiplying equation(1) by `4` We get,

`12x +16y = -56 (3)`

Subtracting equation (3) from equation (2) we get ,

`-19y= =76 or y = -4`

Putting `y=-4` in equation (1) we get,

`3x - 16 =-14 or 3x =2 or x = 2/3`

Solution : `x =2/3 , y = -4` [Ans]

Answer 2

`x = 2/3 and y =-4`

Explanation:

There are at least `5` methods to solve a system of equations:

• eliminating one variable - create additive inverses
• substituting for one variable
• equating two variables
• matrices
• graphically

`color(white)(xxxxx)3xcolor(blue)(+4y) = -14color(white)(xxxxxxxxx)A`
`color(white)(xxxx)12xcolor(blue)(-3y) =+ 20color(white)(xxxxxxxxx)B`

I would choose to eliminate the `y` terms because they have opposite signs and are therefore easy to make into additive inverses. The sum of additive inverses is `0`

The LCM of `3 and 4 " is " 12`

`Axx3: color(white)(xxx)9xcolor(blue)(+12y) = -42color(white)(xxxxxxxxx)C`
`Bxx4:color(white)(xx)48xcolor(blue)(-12y) =+ 80color(white)(xxxxxxxxx)D`

`C+D:color(white)(xx)57x color(white)(xxx)= 38" "larr` the `y`-term is `0`

`color(white)(xxxxxxxxx)x color(white)(xxx)= 38/57`

`color(white)(xxxxxxxxxx)x color(white)(xxx)= 2/3`

Substitute `x = 2/3` into A

`color(white)(xxxxxx)3(2/3)+4y = -14color(white)(xxxxxxxxx)A`

`color(white)(xxxxxxxxxxxxx)4y = -14 -2`
`color(white)(xxxxxxxxxxxxx)4y = -16`
`color(white)(xxxxxxxxxxx.xx)y = -4`