DWG NO. 07 — Unit 7 of 10
5 online lessons · 1 in-person Review & Practice Day
Unit 1 defined a function as a relationship between two quantities and taught you to read its graph. A system of equations just asks about two (or more) of those relationships at once: where, if anywhere, do their graphs agree? This unit opens with the two algebraic tools for pinning down that shared point exactly — substitution and elimination — then extends the idea to systems of inequalities, where the "solution" is a whole shaded region rather than a single point.
The back half introduces the matrix: a rectangular grid of numbers that turns a system's coefficients into an object you can manipulate directly. Matrices let you automate elimination (Gaussian elimination), and their determinant — a single number computed from a matrix — gives a second, purely algebraic route to the same solutions through Cramer's Rule. Symbol-heavy lessons like 7.4 and 7.5 are natural candidates to slow down on; take the extra time if you need it.
Solving Systems by Substitution and Elimination
Finding the intersection point of two linear equations algebraically, and recognizing when there isn't exactly one.
→Systems of Inequalities
Graphing linear inequalities and identifying the region that satisfies every inequality in a system at once.
→Introduction to Matrices and Matrix Operations
Matrix notation and dimension, plus addition, subtraction, scalar multiplication, and matrix multiplication.
→Solving Systems Using Matrices
Writing a system as an augmented matrix and using Gaussian elimination and back-substitution to solve it.
→Determinants and Cramer's Rule
Computing 2×2 and 3×3 determinants and using Cramer's Rule as an alternative way to solve a system.
→Review & Practice Day 7 — bring your questions from lessons 7.1–7.5. You'll work practice problems, get feedback, and take the Unit 7 test.