Question

How do you solve the system `0.5x+4y=-1` and `x+2.5y=3.5` using substitution?

Answer 1

See a solution process below:

Explanation:

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

`0.5x + 4y = -1`

`0.5x + 4y - color(red)(4y) = -1 - color(red)(4y)`

`0.5x + 0 = -1 - 4y`

`color(red)(2) xx 0.5x = color(red)(2)(-1 - 4y)`

`1x = (color(red)(2) xx -1) - (color(red)(2) xx 4y)`

`x = -2 - 8y`

Step 2) Substitute `(-2 - 8y)` for `x` in the second equation and solve for `y`:

`x + 2.5y = 3.5` becomes:

`(-2 - 8y) + 2.5y = 3.5`

`-2 - 8y + 2.5y = 3.5`

`color(red)(2) - 2 - 8y + 2.5y = color(red)(2) + 3.5`

`0 - 8y + 2.5y = 5.5`

`-8y + 2.5y = 5.5`

`(-8 + 2.5)y = 5.5`

`-5.5y = 5.5`

`(-5.5y)/color(red)(-5.5) = 5.5/color(red)(-5.5)`

`(color(red)(cancel(color(black)(-5.5)))y)/cancel(color(red)(-5.5)) = -1`

`y = -1`

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

`x = -2 - 8y` becomes:

`x = -2 - (8 * -1)`

`x = -2 - (-8)`

`x = -2 + 8`

`x = 6`

The Solution Is: `x = 6` and `y = -1` or `(6, -1)`