Question

How do you solve `y=4x` and `x+y=5`?

Answer 1

The common point for these two equations ( where the graphs cross) is:

`x=1`
`y=4`

Explanation:

Given:
`color(blue)(y=4x)` ..................................(1)
`color(brown)(x+y=5)`................................(2)

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To solve for a variable your equation has to end up with just 1 of that variable and no others. That variable has to be on one side of the equals sign and everything else on the others side.

If we substitute for y in equation (2) using what y is worth from equation (1) we have just 1 variable. Which is `x`.

`color(brown)(x+y=5" "->" "x+color(blue)(4x)=5)color(white)(..)...................(2_a)`

But `4x+x=5x`

`x+4x=5" "->" "5x=5`

Divide both sides by 5

`5/5xx x = 5/5`

But `5/5=1`

`x=1`
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Substitute for `x` in equation (1) where `x=1`

`color(brown)(y=4x" "->" "y=4(color(blue)(1))`

In algebra `4x` is the same as `4 xx x`

But `x` has the value of 1 so we have

`y=4xx1`

`y=4`
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Note that `x+y=5` is another way of writing
`y=-x+5`