Q. 4 - Precalculus Enhanced with Graphing Utilities

Question

solve each system of equations using the method

of substitution or the method of elimination. If the system has no

solution, say that it is inconsistent.

$\left\{\begin{array}{l}3x + 2y - 8z = -3\\ -x - \frac{2}{3}y + z = 1\\ 6x - 3y + 15z = 8\end{array}\right.$

Step-by-Step Solution

Answer

The solution of the given equation is $\left(\frac{1}{3},-2,0\right)$

Step 1. Given

$\left\{\begin{array}{l}3x + 2y - 8z = -3\\ -x - \frac{2}{3}y + z = 1\\ 6x - 3y + 15z = 8\end{array}\right.$

Step 2. Calculation

$$\begin{gathered} \left\{\begin{array}{l}3x + 2y - 8z = -3......\left(1\right)\\ -x - \frac{2}{3}y + z = 1..........\left(2\right)\\ 6x - 3y + 15z = 8........\left(3\right)\end{array}\right. \\ consider equation 2 \\ -3x-2y+3z=3 \\ Add eq. 2 with eq. 1 we get \\ -5z=0 \\ z=0 \\ Substituting the value of z in eq.1 and eq.2 we get \\ 3x+2y-8\left(0\right)=-3.....\left(4\right) \\ 6x-3y+15\left(0\right)=8.......\left(5\right) \\ Multiply 3 with eq. 4 and 2 with eq.5and add both \\ 21x=7 \\ x=\frac{1}{3} \\ substitute value of x in eq4. \\ 3\left(\frac{1}{3}\right)+2y=-3 \\ y=-2 \end{gathered}$$