Algebra 1 / Unit 6: Systems of Equations and Inequalities
6.4 Special Systems and Applications
Notes
- Parallel lines (same slope, different intercepts): no solution.
- The same line (same slope and intercept): infinitely many solutions.
- Different slopes: exactly one solution.
- Word problems: name the two unknowns, write two equations (often a total and a value), then solve.
Practice
How many solutions does $y = 2x + 1$ and $y = 2x - 3$ have?
Same slope, different intercepts: parallel lines.
How many solutions does $x + 2y = 4$ and $2x + 4y = 8$ have?
The second equation is the first one doubled.
Adult tickets cost $8 and student tickets $5. 50 tickets sold for $310. How many adult tickets sold?
$a + s = 50$, $8a + 5s = 310$. $8a + 5(50 - a) = 310 \Rightarrow 3a = 60$.
Ready for more? Take the Unit 6 test.