Integrated Math 1 / Unit 6: Systems of Equations and Inequalities
6.1 Solving Systems by Graphing
Notes
A system of equations is two or more equations with the same variables. A solution is an ordered pair that makes every equation true.
- Graph both lines: the solution is where they intersect.
- Lines that cross have one solution. Parallel lines (same slope, different intercepts) have no solution. The same line twice has infinitely many solutions.
- Check a solution by substituting it into both equations.
- Example: $(2, 5)$ solves $x + y = 7$ and $x - y = -3$ because $2 + 5 = 7$ and $2 - 5 = -3$.
Practice
How many solutions does the system $y = 2x + 1$ and $y = 2x - 3$ have?
The lines have the same slope but different $y$-intercepts, so they are parallel.
Which ordered pair is a solution of both $x + y = 7$ and $x - y = -3$?
Only $(2, 5)$ gives $7$ in the first equation and $-3$ in the second.
How many solutions does the system $y = x + 2$ and $2y = 2x + 4$ have?
Dividing the second equation by 2 gives $y = x + 2$, the same line.
Ready for more? Take the Unit 6 test.