Question

How do solve the following linear system?: `5x+2y=1 , 5x-4y=23`?

Answer 1

See below

Explanation:

Basically, You use both equations to find the value of one variable and plug that into one of the equations given to get the value of the other variable.

`5x+2y=1, 5x-4y=23`

Solve equation 1 for `5x`:

`5x=1-2y`

Substitute into second equation:

`1-2y-4y=23`

Solve for `y`

`-6y=22 => color(blue)(y=-22/6=-11/3`

Then use the value of `y` and substitute it into one of the equations and solve for `x`:

`5x+2y=1`

`5x+2(-11/3)=1`

`5x-22/3=1`

`5x=25/3=>color(blue)(x=5/3`

Check by graphing (the circle shows the plotted point `(5/3,-11/3)`

graph{(5x+2y-1)(5x-4y-23)((x-5/3)^2+(y+11/3)^2-.1)=0}