How do you find the solution of the system of equations 5x - 2y = 4 and 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 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!