Question

How do you find the solution of the system of equations `5x - 2y = 4` and `3x + y = 9`?

Answer 1

Find the value of one variable, and use that to solve for the other: See below.

Explanation:

A system of equations can technically be solve via one of 2 methods: elimination (I won't explain that here, since it is impractical, and I don't know that one too well; it makes your life necessarily difficult); substitution, where you isolate one of the variables in either equation (let's say you isolate `x`), and replace `x` in the other equation with the expression that you determined equals `x`. Graphing is good if you're in a pinch, but useless if you don't have a graphing calculator!

I'll demonstrate below:

Substitution (personal recommendation)

Step 1: Isolate one variable in one of the equations

`5x-4y=4`
`3x+y=9`

`5x cancel(-4y) color(blue)(+4y) = 9 color(blue)(+4y)`

`5x color(green)(-9) = cancel(9)+4y color(green)(-9)`

`5/4x-9/4=color(red)(cancel(4)/4)y`

`5/4x-9/4=y`

Now replace `y` in the other equation with `5/4x-9/4`, and solve for `x`

`3x+5/4x-9/4=9`

`12/4x+5/4x-9/4=9`

`17/4x=36/4+9/4`

`17/4x=45/4`

`x=45/4 div17/4`

`x=(45times4)/(4 times17)`
`x=(45timescancel4)/(cancel4 times17)`

`x=45/17`

And solve for `y`

`3(45/17)-9=y`

`x=45/17` and `y=-18/17`

Hope that helps!