Question

How do you solve the system of equations `y= 10x - 10` and `y = \frac { - 2} { 3} x + \frac { 1} { 7}`?

Answer 1

`x = 213/224 and y = -55/112`

Explanation:

This type of question is often asked when you are working with straight line equations.

This is a GREAT way to have the question asked because both equations have `y` as the subject.

Note that the value of `y` will be the same in each case.

`color(blue)(y = (-2)/3x +1/7)" and "color(red)( y = 10x-10)`

`color(white)(............................)color(blue)(y) = color(red)( y )`

`color(white)(.........)color(blue)((-2)/3x +1/7)" = "color(red)(10x-10)`

Multiply through by `21` to cancel the denominators

`color(green)(cancel21^7xx)(-2)/cancel3x +color(green)(cancel21^3xx)1/cancel7" = "color(green)(21xx)10x-color(green)(21xx)10`

`color(white)(.........................)-14x+3" = "210x-210`

`color(white)(.............................)3+210" = "210x+14x`

`color(white)(...................................)213" = "224x`

`color(white)(...................................)213/224" = "x`

Now that you have a value for `x`, substitute into either of the original equations to find `y`.

`color(red)( y = 10x-10)`

`y = 10(213/224)-10`

`y = -55/112`