Question

8 a system of equations is given. \\(\

$$\begin{cases} 3x + y = 6 \\\\ 6x - y + 4z = 13 \\\\ 7x + 2z = 7 \\end{cases}$$

\\) what is the x - value of the solution to the system? \\(\boldsymbol{\text{\\(\circled{a}) } - 1}) \\(\boldsymbol{\text{\\(\circled{b}) } 9}) \\(\boldsymbol{\text{\\(\circled{c}) } 7}) \\(\boldsymbol{\text{\\(\circled{d}) } - 5})

Explanation:

Step1: Add first two equations

Add \(3x + y = 6\) and \(6x - y + 4z = 13\) to eliminate \(y\).
\((3x + y)+(6x - y + 4z)=6 + 13\)
Simplify: \(9x+4z = 19\)

Step2: Solve the system of two equations

We have two equations:

1. \(9x + 4z = 19\)
2. \(7x + 2z = 7\) (multiply this equation by 2: \(14x+4z = 14\))

Subtract the first new equation from the second new equation:
\((14x + 4z)-(9x + 4z)=14 - 19\)
Simplify: \(5x=-5\)

Step3: Solve for x

Divide both sides by 5: \(x=\frac{-5}{5}=-1\)

Answer:

A. \(-1\)