### Home > CCA2 > Chapter 9 > Lesson 9.2.1 > Problem 9-53

9-53.

Solve the system of equations below. Homework Help ✎

8

*x*− 3*y*− 2*z*= −8

−2*x*+ 8*y*+ 7*z*= 26

4*x*+*y*− 5*z*= 23

Multiply the 2^{nd} equation by 4 and add to the 1^{st}.

29*y* + 26*z* = 96 (Eq. #4)

Multiply the 2^{nd} equation by 2 and add to the 3^{rd}.

17*y* + 9*z* = 75 (Eq. #5)

Multiply the 5^{th} equation by 26.

442*y* + 234*z* = 1950

Multiply the 4^{th} equation by −9.

−261*y* − 234*z* = −864

Subtract the two equations eliminating *y*. Solve for *y*.

181*y* = 1086

*y* = 6

Use substitution to find *x* and *y*. Check your answers in all three equations!