Dependent Systems
Solve dependent systems in Grade 9 math — The equations are called dependent equations, and they have identical solution sets because their graphs are t
Key Concepts
Property Dependent systems have an infinite number of solutions. The equations are called dependent equations , and they have identical solution sets because their graphs are the same line.
Explanation It's like having two secret identities that are actually the same person! When you solve these systems, the variables vanish and you're left with a true statement, like $6 = 6$. This means the equations are identical and describe the exact same line, so any point on that line is a valid solution.
Examples The system $x + 3y = 6$ and $\frac{1}{3}x + y = 2$ simplifies to two identical equations: $y = \frac{1}{3}x + 2$. Solving the system $x + 3y = 6$ and $\frac{1}{3}x + y = 2$ using substitution leads to $x + 3(2 \frac{1}{3}x) = 6$, which simplifies to the true statement $6=6$. The equations $x + y = 10$ and $ x y = 10$ are identical, because multiplying the second equation by $ 1$ results in the first equation.
Common Questions
What is 'Dependent Systems' in Grade 9 math?
The equations are called dependent equations, and they have identical solution sets because their graphs are the same line. Explanation It's like having two secret identities that are actually the same person!.
How do you solve problems involving 'Dependent Systems'?
Explanation It's like having two secret identities that are actually the same person! When you solve these systems, the variables vanish and you're left with a true statement, like $6 = 6$.
Why is 'Dependent Systems' an important Grade 9 math skill?
Remember, `c` is ALWAYS the hypotenuse (the longest side, across from the right angle).. If you accidentally put a leg's length in for `c`, your answer will be incorrect.