The following system of linear equations is g | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(D) Given equations are:$2x + 3y + 2z = 9 \quad (1)$$3x + 2y + 2z = 9 \quad (2)$$x - y + 4z = 8 \quad (3)$Subtracting equation $(1)$ from equation $(2

Vedclass · Accepted Answer

has a unique solution

Vedclass · Answer

(D) Given equations are:$2x + 3y + 2z = 9 \quad (1)$$3x + 2y + 2z = 9 \quad (2)$$x - y + 4z = 8 \quad (3)$Subtracting equation $(1)$ from equation $(2)$:$(3x + 2y + 2z) - (2x + 3y + 2z) = 9 - 9$$x - y = 0 \Rightarrow x = y$Substitute $x = y$ into equation $(3)$:$x - x + 4z = 8 \Rightarrow 4z = 8 \Rightarrow z = 2$Substitute $z = 2$ into equation $(1)$:$2x + 3y + 2(2) = 9$$2x + 3y = 5$Since $x = y$,we have $2x + 3x = 5 \Rightarrow 5x = 5 \Rightarrow x = 1$Thus,$x = 1, y = 1, z = 2$.The system has a unique solution $(1, 1, 2)$.

The following system of linear equations is given: $2x + 3y + 2z = 9$,$3x + 2y + 2z = 9$,and $x - y + 4z = 8$. Which of the following statements is true?

Similar Questions

If $\begin{bmatrix} 1 & 3 & 3 \\ 1 & 4 & 4 \\ 1 & 3 & 4 \end{bmatrix} \begin{bmatrix} x \\ y \\ z \end{bmatrix} = \begin{bmatrix} 12 \\ 15 \\ 13 \end{bmatrix}$,then the value of $x^2 + y^2 + z^2 =$

Solve the system of linear equations using the matrix method: $2x + 3y + 3z = 5$,$x - 2y + z = -4$,$3x - y - 2z = 3$.

The number of solutions of the following system of linear homogeneous equations $x-y+z=0$,$x+2y-z=0$,and $2x+y+3z=0$ is

Identify the correct statement:

Vedclass Test Series

Exam Paper Generator

Online Exam Module