Chapter 1
Numbers and Operations
Course: Gace Middle Grades Math 4 8 704
Subject: Gace Middle Grades Math 4 8 704
Chapter: Algebra
1. Solves a system of two linear equations or inequalities in two variables algebraically and graphically
A system of two linear equations represents two straight lines in the xy-plane. The solution corresponds to the point of intersection, if it exists.
Algebraic solution methods:
- Substitution: solve one equation for one variable, then substitute into the other. Example: y = 2x + 1 and x + y = 7 Substitute y: x + (2x + 1) = 7 → 3x + 1 = 7 → x = 2. Then y = 2(2) + 1 = 5. Solution is (2, 5).
- Elimination: add or subtract equations to eliminate one variable. Example: 2x + y = 10 and 3x – y = 5 Add: 5x = 15 → x = 3. Then 2(3) + y = 10 → y = 4. Solution is (3, 4).