How do you find the solution of the system of equations 5x - 2y = 4 5x2y=4 and 3x + y = 9 3x+y=9?

1 Answer
May 5, 2018

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 xx), and replace xx in the other equation with the expression that you determined equals xx. 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=45x4y=4
3x+y=93x+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!