Question

How do you determine the solution in terms of a system of linear equations for `1/2x = 4y`, `5y - x = -3`?

Answer 1

`x=8`
`y=1`

Explanation:

I think the easiest method for solving this system is through substitution.

So we are given two equations:
`1/2x=4y`
`5y−x=−3`

Let's get the value of `x` in the first equation:
`1/2x=4y`
`(2)(1/2x)=(2)(4y)`
`color(blue)(x=8y)`

Now let's substitute this into the second equation:
`5y−color(blue)(x)=−3`
`5y−color(blue)((8y))=−3`
`-3y=−3`
`(-1/3)(-3y)=(-1/3)(−3)`
`(-1/3)(-3y)=(-1/3)(−3)`
`color(red)(y=1)`

Now that we know the `y` value, we can solve for the `x` value:
`color(blue)(x=8)color(red)y`
`color(blue)(x=8)color(red)((1))`
`color(blue)(x=8)`

So the solution of the system is:
`color(blue)(x=8)`
`color(red)(y=1)`