Solve the following system of linear equations by the elimin

Solve the following system of linear equations by the elimination method. (If there is no solution, enter NO SOLUTION for each answer. If there are infinitely many solutions, enter INFINITELY MANY for each answer.)

Solution

We have - 1/7 x - 1/2 y = - 2/3 . On multiplying both the sides by - 42, we get 6x + 21y = 28...(1)

We also have - 4/7 x - 2y = - 8/3 . On multiplying both the sides by - 21, we get 12x + 42y = 56 . Now, on dividing both the sides by 2, we get 6x + 21y = 28...(2) We observe that the equations 1 and 2 are identical. Therefore, the given equations are also identical. This being a system of one equation in 2 variables, will have infinitely many solutions. The solution is 6x = 28 - 21y or, x = 1/6( 28 - 21y) = 14/3 - 7/2y. Now by assigning arbitrary values of y, we get the corresponding values of x.