Question

How do you solve this system of equations: `5x + y = 0; 7x + 3y = 0`?

Answer 1

See a solution process below:

Explanation:

Step 1) Solve the first equation for `y`:

`5x + y = 0`

`5x - color(red)(5x) + y = 0 - color(red)(5x)`

`0 + y = -5x`

`y = -5x`

Step 2) Substitute `(-5x)` for `y` in the second equation and solve for `x`:

`7x + 3y = 0` becomes:

`7x + 3(-5x) = 0`

`7x + (-15x) = 0`

`7x - 15x = 0`

`(7 - 15)x = 0`

`-8x = 0`

`(-8x)/color(red)(-8) = 0/color(red)(-8)`

`(color(red)(cancel(color(black)(-8)))x)/cancel(color(red)(-8)) = 0`

`x = 0`

Step 3) Substitute `0` for `x` in the solution to the first equation at the end of Step 1 and calculate `y`:

`y = -5x` becomes:

`y = -5 xx 0`

`y 0`

The Solution Is:

`x = 0` and `y = 0`

Or

`(0, 0)`