Question

How do you solve the following system: # 8x-7y=-39, 5x-9y=-23 #?

Answer 1

`x = -190/37 and y = -11/37`

Be sure to work with fractions, not decimals which will be recurring and will require rounding, leading to inaccurate answers.

Explanation:

The ideal scenario is to have the numerical coefficients of one of the variables as additive inverses.

`" "color(blue)(8)x-7y =-39" "............................A`
`" "color(red)(5)x-9y=-23" "............................B`

`A xx 5" "color(blue)(40)x-35y =-195" "............................C`
`B xx "-"8" "color(red)("-"40)x+72y =+184" "............................D`

Add the equations:

`C+D:" "37y = -11" "larr x` is eliminated

`color(white)(...............................)y = -11/37`

Now substitute the value for `y` into one of the equations

In `A:" "8x-7(-11/37) =-39`

`8x +77/37 = -39`

`8x = -39-77/37`

`8x = -39-2 3/37`

`8x = -41 3/37`

`8x = -1520/37`

`x =-1520/(8xx37)`

`x = -190/37`

Who comes up with these equations???