Question

Find all solutions of the given system of equations and check your answer graphically. HINT [See Examples 1-4.] (If there is no solution, enter NO SOLUTION. If the system is dependent, express your answer in terms of x, where y = y(x).)

3x − 4y= 4
9x − 12y= 12

Answer 1

`Infinitely\ many\ solutions\ exist.\\\\Solutions\ are\ (x,(3)/(4)x-1)`

Explanation:

`Given\ equations\ are\\\\3x-4y=4.................eq(1)\\\\9x-12y=12..............eq(2)\\\\divide\ eq(2)\ by\ 3\\\\(1)/(3)(9x-12y=12)\\\\\Rightarrow 3x-4y=4\\\\Hence\ equations\ represent\ the\ same\ line.\\Hence\ Infinitely\ many\ solutions\ exist.\\\\3x-4y=4\\\\4y=3x-4\\\\y=(3)/(4)x-1\\\\Solutions\ are\ (x,(3)/(4)x-1)`