3.2 Solving Systems Algebraically
In reality, serendipity accounts for one percent of
the blessings we receive in life, work and love. The
other 99 percent is due to our efforts.

Solving Systems by Substitution
Substitution Method: Solving a system of equations by replacing one
variable with an equivalent expression containing the other variable.
Ex1) y  4 x  8
y  x7
Ex2) 2y  3x  4
6x  y  7

Solving Systems by Elimination
Elimination Method: A method for solving a system of equations by
adding two equations to eliminate a variable. (aka…“stack-n-add”)
Ex3) 5 x  6 y  32
3x  6 y  48
Ex4)  2 x  5 y  22
10 x  3 y  22
Solving Systems by Elimination
15 x  3 y  9
Ex5)
10 x  7 y  4
Eliminate x 1st…
Eliminate y 1st…
Systems Without a Unique Solution
Ex6) 3x  5 y  7
6 x  10 y  14
Ex7)
2 x  4 y  6
3x  6 y  8
Solving Systems ~ Application
Ex8) A school is bringing 193 total people to a competition. There are 8
drivers to drive buses and minivans. If buses seat 51 and minivans seat 8,
how many buses and minivans are needed?
Substitution:
Elimination:
3.2 Solving Systems Algebraically
HW: 1-10 first column, 11,
18, 21, 30-39 first column,
42, 45, 48, 49, 62
In reality, serendipity accounts for one percent of
the blessings we receive in life, work and love. The
other 99 percent is due to our efforts.