Answer
No Solution.
Solution set:$\{\}$
Work Step by Step
$5y-7z=14$ Equation $(1)$
$2x+y+4z=10$ Equation $(2)$
$2x+6y-3z=30$ Equation $(3)$
Multiply Equation $(2) $ by $-6$ and add with Equation $(3)$
$-6(2x+y+4z)+2x+6y-3z=-6(10)+30$
$-12x-6y-24z+2x+6y-3z = -60+30$
Combine like terms.
$-10x-27z=-30$ Equation $(4)$
Multiply Equation $(2) $ by $-5$ and add with Equation $(1)$
$-5(2x+y+4z)+5y-7z=-5(10)+14$
$-10x-5y-20z+5y-7z=-50+14$
Combine like terms.
$-10x-27z=-36$ Equation $(5)$
Subtract Equation $(5)$ from Equation $(4)$
$-10x-27z-(-10x-27z)=-30-(-36)$
$-10x-27z+10x+27z=-30+36$
Combine like terms.
$0=6$
Since the statement is false, the equations are inconsistent and parallel. Therefore, the system has no solution.
Solution set:$\{\}$
