Solve the system If the system has infinitely many solutions

Solve the system. (If the system has infinitely many solutions, express your answer in terms of k, where x = x(k) and y = k. If there is no solution, enter NO SOLUTION.) {7x - 5y = 10 3x + 2y = 6

Solution

7x - 5y = 10 .....................[1]

3x + 2y = 6 ......................[2]

equation [2] can be written as:

2y = 6 - 3x

=> y = (6 - 3x)/2

=> y = 3 - 1.5x

substituting this in equation [1] we get:

7x - 5[3 - 1.5x] = 10

=> 7x - 15 + 7.5x = 10

=> 7x + 7.5x = 10 + 15

=> 14.5x = 25

=> x = 1.724

substituting this in equation [2] we get:

y = 3 - 1.5[1.724] = 0.414

so, (x,y) = (1.724, 0.414).