48 x - 72 y = 30 y + 24 r y = 1 6 - 16 x In the

Question

48 x - 72 y = 30 y + 24 r y = 1 6 - 16 x In the given system of equations, r is a constant. If the system has no solution, what is the value of r ?

Accepted Answer

The correct answer is - 34 . A system of two linear equations in two variables, x and y , has no solution if the lines represented by the equations in the xy -plane are distinct and parallel. Two lines represented by equations in standard form A x + B y = C , where A , B , and C are constants, are parallel if the coefficients for x and y in one equation are proportional to the corresponding coefficients in the other equation. The first equation in the given system can be written in standard form by subtracting 30 y from both sides of the equation to yield 48 x - 102 y = 24 . The second equation in the given system can be written in standard form by adding 16 x to both sides of the equation to yield 16 x + r y = 1 6 . The coefficient of x in this second equation, 16 , is 1 3 times the coefficient of x in the first equation, 48 . For the lines to be parallel the coefficient of y in the second equation, r , must also be 1 3 times the coefficient of y in the first equation, - 102 . Thus, r = 1 3 ( - 102 ) , or r = - 34 . Therefore, if the given system has no solution, the value of r is - 34 .

Question 48-x-7