Algebra 2/Trig
Name: ________________________________
Section 3.1 Notes: Solving Systems of Equations p. 156
+Learning Target: I can solve and classify Systems of Equations by Graphing.
VOCABULARY
System of two linear equations- Two equations, with the variables x and y.
Solution of a system- An ordered pair (x, y) that satisfies each equation
Consistent- A system that has ____________________________ solution
Inconsistent- A system that has _________ solution
Independent- A consistent system that has exactly _________ solution
Dependent- A consistent system that has __________________________ solutions
THE GRPAHING METHOD
NUMBER OF SOLUTIONS OF A LINEAR SYSTEM
Exactly one solution
Infinitely many solutions
No Solutions
Lines intersect at one point:
CONSISTENT and
INDEPENDENT
Lines coincide: CONSISTENT
and DEPENDENT
Lines are parallel:
INCONSISTENT
EXAMPLE 1: Graph and Classify
𝑥+𝑦 =5
Graph: {
𝑥 − 5𝑦 = −7
Solution:
Classify:
Check:
1
+Checkpoint 1: Graph and classify: {
2𝑥 + 3𝑦 = 1
then find the solution from the graph.
−3𝑥 + 4𝑦 = −10
THE SUBSTITUTION METHOD
Learning Target: Solve Systems of Equations by Substitution
Step 1 Solve one of the equations for one of its variables (if not done so already)
Step 2 Substitute the expression from Step 1 into the other equation and solve for the other variable.
Step 3 Substitute the value from Step 2 into the revised equation from Step 1 and solve.
EXAMPLE 2: Solve by Substitution
{
3𝑥 + 𝑦 = 8
18𝑥 + 2𝑦 = 4
2
EXAMPLE 3: Solve by Substitution
2𝑥 + 3𝑦 − 2𝑧 = 4
{3𝑥 − 3𝑦 + 2𝑧 = 16
2𝑧 = −5
𝑎+𝑏+𝑐 =6
+Checkpoint 2: Use substitution to solve the system of equations: {3𝑎 − 𝑏 + 𝑐 = 8
2𝑏 = 𝑐
EXAMPLE 4: Mixture Problem
If a 20% acid solution is mixed with a 5% acid solution, how much of each solution is needed to make 150
mL of a 15% acid solution (to nearest mL)?
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HW: Pages 161 – 163. Problems 12 - 48 (3rds), 54 – 59 ALL
3