Question

How do you solve the following system: `3x - 4y = -10, 4x + 7y = 6x`?

Answer 1

`x=-70/13" "`I have left the derivation of y for the reader to determine.

Explanation:

Given:

`3x-4y=-10" "`.................................(1)
`4x+7y=6x" "`......................................(2)
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Consider equation (2)

Subtract `4x` from both sides

`7y=2x`

Divide both sides by 7

`y=2/7x" "......................................(2_a)`

Substitute `(2_a)" into "(1)`

`3x-4(2/7x)=-10" "...................(1_a)`

`3x-8/7x=-10`

`x(21-8)/7=-10`

`x=-(7/13xx10)`

`x=-70/13" ".......................................(1_b)`
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

You can now find `y` by substituting `(1_b)` into either of (1) or (2).

I will leave that for the reader to do