Solving Systems of Equations with 2 Variables

Hi all. This is Brad.


Solving systems of linear equation by substitution

Steps for solving 2 equations, 2 unknowns using the substitution method
(those are in booklet)

1. Solve one of the equation to figure out one of the variables.

2. Substitute the equation into other equation and solve for second variables.

3. Substitute the value into either equation and solve for first variable.

4. State answer as an ordered pair.

5. Check.

Here is an example

2x – 3y = –2
4x + y = 24

Idea here is to solve one of equation for one of variables, and plug it into other equation. It doesnt matter which equation or variable you pick, there are no right or wrong choice but however some choices can be better than others.

For me I would pick the second equation and transform it into Y intercept form.

4x + y = 24
y = –4x + 24


Now plug that into other equation

2x – 3(–4x + 24) = –2
2x + 12x – 72 = –2
14x = 70
x = 5

Plug x value into either equation

2x - 3y = -2


2(5) - 3y = -2
10 - 3y = -2
-3y = -2 - 10
-3y = -12 / -3


and both sides divided by -3 gives us y = -12 over -3 which is


y = 4

There you have y value too. State both X and Y as an ordered pair and put both X and Y into either equation and check if that works correctly.