Question

Determine the nature equation
2x + y =5

4×+2y{10​

Answer 1

The given system of equations is:  2x + y – 5 = 0  4x + 2y – 10 = 0  The above equations are of the form  a1 x + b1 y − c1 = 0  a2 x + b2 y − c2 = 0  Here, a1 = 2, b1 = 1, c1 = −5  a2 = 4, b2 = 2, c2 = −10 So according to the question, we get  a1a2a1a2 = 2424 = 1212  b1b2b1b2 = 1212 and,  c1c2c1c2 = −5−10−5−10 = 1212  ⇒ a1a2a1a2 = b1b2b1b2 = c1c2c1c2  Hence, we can conclude that the given system of equation has infinity many solutions.