Question

the linear system
\\(-4x + 2y = 16\\)
\\(-7x - 6y = -29\\)
can be written as the following augmented matrix. solve for \\(x\\) and \\(y\\).

\\
\left\

$$\begin{array}{cc|c} -4 & 2 & 16 \\\\ -7 & -6 & -29 \\end{array}$$

\
ight
\\

\\(x = \\)
\\(y = \\)

Explanation:

Step1: Write down the system of equations

The system of linear equations is:

$$
LATEXBLOCK0
$$

Step2: Eliminate one variable by scaling

Multiply the first equation by \(3\) to align coefficients:

$$-12x + 6y = 48$$

Step3: Add the equations to solve for \(x\)

Add the scaled equation to the second equation:

$$(-12x + 6y) + (-7x - 6y) = 48 - 29$$

$$-19x = 19$$

$$x = -1$$

Step4: Substitute \(x\) back to find \(y\)

Substitute \(x = -1\) into the first equation:

$$-4(-1) + 2y = 16$$

$$4 + 2y = 16$$

$$2y = 12$$

$$y = 6$$

Answer:

\(x = -1\)
\(y = 6\)