Algebra 3 VIDEO NOTES:
Sec. 12.1 Solving systems with Substitution & Elimination
A _______________ of equations is a collection of two or more equations, with one or more variables.
Categorizing the Systems:
Inconsistent:
Systems that are
parallel; same slope
Dependent or Consistent:
Systems that overlap;
Same line & share ALL points
Independent:
Systems that intersect once;
solution is point of intersection
Solution: ________________
Solution: ________________
Solution: ________________
Identifying Solutions:
Substitution:
Solve for one variable in terms
of the other and substitute in
the remaining equation.
Elimination:
Multiply or divide to obtain
coefficients that will be negatives
of each other.
Solve & use back-substitution
to solve for the initial variable
Add the equations, solve, and use
back-substitution to solve for
the other variable.
(Graphing or Matrices)
Solve the following systems:
5𝑥 − 𝑦 = 13
2𝑥 + 3𝑦 = 12
Example 1: {
2𝑥 + 𝑦 = 1
4𝑥 + 2𝑦 = 3
Example 2: {
𝑥 + 2𝑦 = 4
Example 3: {
2𝑥 + 4𝑦 = 8
𝑥−𝑦−𝑧 =1
Example 4: {2𝑥 + 3𝑦 + 𝑧 = 2
3𝑥 + 2𝑦 = 0
5. With a tail wind, a small Piper aircraft can fly 600 miles in 3 hours. Against this same wind, the Piper can fly
the same distance in 4 hours. Find the average wind speed and the average airspeed of the Piper.
6. A movie theater sells tickets for $8.00 each, with seniors receiving a discount of $2.00. One evening the
theater sold 525 tickets and took in $3580. in revenue. How many of each type of ticket were sold?
CLASSWORK: SHOW ALL WORK FOR CREDIT
Pages 847-849 # 8, 18, 23, 26, 38, 62, 63, 64, 65