Question

Without graphing, classify the system as independent, dependent, or inconsistent: {x - 5 = -y 2y - 10 = -2x a) Independent b) Dependent c) Inconsistent

Answer 1

Answer B

Explanation:

If a consistent system has exactly one solution, it is independent . If a consistent system has an infinite number of solutions, it is dependent . When you graph the equations, both equations represent the same line. If a system has no solution, it is said to be inconsistent .

`\left\{\begin{array}{ccc}x-5&=&-y\\2y-10&=&-2x\\\end {array} \right.\\\\\\\left\{\begin{array}{ccc}x+y&=&5\\2x+2y&=&10\\\end {array} \right.\\\\\\\left\{\begin{array}{ccc}x+y&=&5\\x+y&=&5\\\end {array} \right.\\\\\\`

Answer : system is dependent because infinity solutions