The correct option is (C) No solution.
Step-by-step explanation: We are given to find the solution of the following system of equations :
Dividing equation (i) by 3 on both sides, we get
Substituting the value of y from equation (iii) in equation (ii),we get
which CANNOT be true.
So, the given system of equations will have no solution.
Option (C) is CORRECT.
Please, separate equations with a comma, or the word "and," or a semicolon.
Next, determine the LCD and multiply both equations by it, so as to elimiinate the fractional coefficients.
should be written as the system
3y=(3/2)x+6 Use parentheses around the fraction for clarity
(1/2)y-(1/4)x=3 Same: use parentheses
The LCDs here are 2 (for the first equation) and 4 (for the second equation). Multiply the first equation by 2 to eliminate the fractions:
3y=(3/2)x+6 → 6y = 3x + 12, and
4[ (1/2)y-(1/4)x=3 ] → 2y - x = 12
Let's use the substitution method to solve this system. Solve the 2nd equation for x, obtaining x = 2y - 12. Substitute 2y - 12 for x in the 1st equation 6y = 3x + 12:
6y = 3(2y - 12) + 12, or
6y = 6y - 36 + 12
This reduces to 0 = -24, which is never true. Thus,
this system has NO solution.
C.) no solution