Final Answer:
This system of linear equation has one unique solution as the coefficients of both equations are not equal.
Step-by-step explanation:
To determine if a unique solution exists for a system of linear equation, we use the concept of determinants. A linear equation system is said to have a unique solution if the determinant of coefficients in the equation is not equal to zero. Determinant of a matrix is calculated by using the concept of cross multiplication and subtracting the product of the diagonals on the opposite sides.
For the given system of equations, 12x1 + 7x2 = 147 and 15x1 + 9x2 = 168, the determinant of the coefficients is calculated as follows: 12 x 9 - 7 x 15 = 63. Since the value of the determinant is not zero, the system of equation has one unique solution.
By using the concept of elimination, the value of both x1 and x2 can be determined. In this method, the coefficient of one of the variables is made same in both equations by multiplying the equations with suitable coefficients. Then, the value of the same variable is eliminated in one of the equations. After that, the value of the other variable can be determined by substituting the value of the eliminated variable in the other equation. Finally, both the values of x1 and x2 can be substituted in the original equations to determine the final unique solution.
Thus, we can conclude that this system of linear equation has one unique solution.