Question

Which of the following system of linear equations has no solution 1. x =3 y= 5 2. y 6x+6 y=5x+6 3. y =16X +3 y=16x +19 4.

y=5 y= 5x+5

Answer 1

HI,

`\left\{\begin{array}{ccc}y&=&16x+3\\y&=&16x+19\\\end{array} \right. \ has \ no\ solution\\`

Explanation:

`\left\{\begin{array}{ccc}x&=&3\\y&=&5\\\end{array} \right.has \ the\ solution\ {(3,5)}\\\\\\\left\{\begin{array}{ccc}y&=&6x+6\\y&=&5x+6\\\end{array} \right.\\\\\left\{\begin{array}{ccc}0&=&x+0\ substract\ both\ equations\\y&=&5x+6\\\end{array} \right.\\\\\left\{\begin{array}{ccc}x&=&0\\y&=&6\ substitue\ the\ value\ of\ x \\\end{array} \right.\ has \ the\ solution\ {(0,6)}\\`

`\left\{\begin{array}{ccc}y&=&16x+3\ (1)\\y&=&16x+19\ (2)\\\end{array} \right.\\\\\left\{\begin{array}{ccc}0&=&0-16\ substract\ (2)\ from\ (1)\\y&=&16x+19\\\end{array} \right.\ \\has \ no\ solution\ \\\\\\`

`\left\{\begin{array}{ccc}y&=&5\ (1)\\y&=&5x+5\ (2)\\\end{array} \right.\\\\\\\left\{\begin{array}{ccc}0&=&5x\ (2)-(1)\\y&=&5x+5\ (2)\\\end{array} \right.\\\\\left\{\begin{array}{ccc}x&=&0\\y&=&5\\\end{array} \right.\ has\ the\ solution\ {(0,5)}`

Answer 2

The system of linear equations that has no solution is the fourth one: y = 5 and y = 5x + 5. This is because the second equation contradicts the first equation, indicating that there is no consistent solution that satisfies both equations simultaneously.