Question

2x-3y=6 4x-6y=9 check whether the following equations are consistent or inconsistent. solve them graphically.​

Answer 1

Answer:

Step-by-step explanation:

y = $m_{1}$ x + $b_{1}$

y = $m_{2}$ x + $b_{2}$

1). System of linear equations is consistent:

(a). System of linear equations is consistent independent , if it has only 1 solution. In this case $m_{1}$ ≠ $m_{2}$

(b). System of linear equations is consistent dependent , if it has infinitely many solutions. In this case $m_{1}$ = $m_{2}$ and $b_{1}$ = $b_{2}$

2). System of linear equations is inconsistent, if it has no solutions. In this case $m_{1}$ = $m_{2}$ and $b_{1}$ ≠ $b_{2}$

~~~~~~~~~~~~~~~~~~~~~~~~~~

2x - 3y = 6  ⇒  y = $\frac{2}{3}$ x - 2

4x - 6y = 9  ⇒  y = $\frac{2}{3}$ x - $\frac{3}{2}$

This system of linear equations is inconsistent, $m_{1}$ = $m_{2}$ = $\frac{2}{3}$ and $b_{1}$ ≠ $b_{2}$ ;

Lines are ║