1. Objective #20: Solve systems of equations by substitution
You are given a set of 2 equations and asked to find the ordered pair that is the solution.
Ex. 3x + 4y = −22
x + 5y = −22
One method of doing this is to use the substitution method. Steps:
rearrange one of the equations to solve for one of the variables. Ex. x = −22 − 5y
substitute that expression into the other equation for the same variable. Ex. 3(−22 − 5y) + 4y = −22

2. Solve the equation for the first variable.
ex. −66 − 15y + 4y = −22
−11y = 44
y = −4
Put that number into one of the original equations to solve for the other variable
ex. x + 5(−4) = −22
x − 20 = −22
x = −2
So the solution is (−2, −4)

3. Note: If after substitution you wind up with an equation that is never true, then the system is inconsistent (no solution). If you wind up with an equation that is always true, then the system is dependent (infinite solutions)