Question

How do you solve the system of equations `5x - y = - 26` and `- 4x - 6y = 1.4`?

Answer 1

`x = -787/170 and y = 97/34`

Explanation:

There are different methods, but in this case, because of the single `y` term, I will use substitution.

`5xcolor(red)(-y) =-26" "and " "-4x-6y =1.4`

`color(red)(5x+26 = y)" "and " "-4x-6color(red)(y) =1.4`
`color(white)(wwwwwwwwwwwwwwwwwwwwwwww)darr`
Replace `color(red)(y)` in the second equation with `color(red)((5x+26))`

`-4x-6color(red)((5x+26)) =1.4`

`-4x -30x -156 = 1.4`

`-34x =1.4+156`

`-34x = 157.4" "larr div-34`

`x = -787/170" "larr` fraction is more accurate than a decimal.

Now find the value of `y` using `y = 5x+26`

`y = 5xx -787/170+26`

`y= 97/34`

Check:

`-4(-787/170) -6(97/34)`

Note: What an awful question!
Trying to do this question without a scientific calculator would be really time-consuming. Do not be tempted to use decimals, they would have to be rounded off, which would mean inaccurate answers.