Solve the following system by the substitution method Check

Solve the following system by the substitution method. Check the solution(s). 3x + y = 24 y= 3x Select the correct choice below and, if necessary, fill in the answer box to complete your answer. A. system has a single solution. The solution set is (Simplify your answer Type an ordered pair) There are infinitely many solutions The solution set is {(x, y) | 3x+ y = 24}. The solution set is the empty set

Solution

We have given the system of linear equations:-

3x+y = 24 --------------------(1)

y= 3x ----------------------(2)

Substitute the value of y= 3x in equation (1), we get

3x + 3x = 24

=> 6x = 24

=> x= 24/6 = 4

plugging value of x= 4 in equation 2, we have

y= 3*4 = 12

Therefore the system has a single solution. The solution set is (4, 12)