math help please!

Question

Solve the system of linear equations and check any solutions algebraically. (If there is no solution, enter NO SOLUTION. If the system is dependent, express x, y, and z in terms of the parameter a.)

2x	+	4y	−	z	=	7
2x	−	4y	+	2z	=	0
x	+	4y	+	z	=	3

Answer 1

I used determinants to solve this set.

The determinant of the coefficients is not 0; therefore, there is a unique solution.

The solution set is x=-2/3, y=3/2 and z = -7/3.

If you don't know how to use determinants,then get z immediately by subtracting the 1st equation from the second

Then subtract the 3rd equation from the 2nd which gives x+z = 3. Since you already know z, this gives you x.

Then the value of y can be determined from any one of the 3 equations.