Solving Linear Systems
Aligned to A-REI.C.6 — Common Core State Standards for Mathematics.
What this lesson teaches
A system of two lines is solved by finding the point that satisfies both equations — use substitution or elimination. That point is where the lines intersect.
Worked examples
Example 1
Solve y = 2x and x + y = 9 by substitution. Replace y: x + 2x = 9, so 3x = 9 and x = 3. Then y = 2(3) = 6. The solution is (3, 6).
Example 2
Parallel lines give no solution: y = 2x + 1 and y = 2x + 5 never meet.
Example 3
Identical lines give infinitely many. If elimination leaves 0 = 0, the two equations were the same line.
Practice questions
- Solve y = x + 1 and y = 2x − 3.
- Solve x + y = 5 and 2x − y = 4.
- Solve 3x + 2y = 12 and x = 2.
Watch the lesson
Every lesson comes with a video taught in English and Spanish — the same video the QR code in the printed workbook opens.
▶ Watch this lessonEn español
Resolver Sistemas Lineales
Un sistema de dos rectas se resuelve hallando el punto que cumple ambas ecuaciones: usa sustitución o eliminación. Ese punto es donde las rectas se cruzan.
Ejemplo 1: Resuelve y = 2x y x + y = 9 por sustitución. Reemplaza y: x + 2x = 9, así que 3x = 9 y x = 3. Luego y = 2(3) = 6. La solución es (3, 6).
Ejemplo 2: Las rectas paralelas no dan solución: y = 2x + 1 e y = 2x + 5 nunca se cruzan.
Ejemplo 3: Rectas idénticas dan infinitas. Si la eliminación deja 0 = 0, las dos ecuaciones eran la misma recta.
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