$$ 2 x-7 z=5 y+14 $$ Solve for $$ x $$ only using Crammer's rule. Expand along ROW1 only. (10)

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We start with the given equation  
$$
2x - 7z = 5y + 14.
$$

Step 1. Write the equation in “matrix form” for the unknown $$x$$. Although there are three variables, we wish to solve only for $$x$$. To do this we isolate the term in $$x$$; that is, we rewrite the equation as  
$$
2x = 5y + 7z + 14.
$$
This can be seen as a 1×1 system  
$$
[2]\, x = 5y + 7z + 14.
$$

Step 2. In Cramer’s rule the solution for $$x$$ is given by  
$$
x = \frac{D_x}{D},
$$
where 
- $$D$$ is the determinant of the coefficient matrix, and  
- $$D_x$$ is the determinant of the matrix obtained by replacing the column for $$x$$ with the constant terms.

Since our coefficient matrix is  
$$
\left[2\right],
$$
its determinant is  
$$
D = 2.
$$

Step 3. The determinant for $$x$$ is obtained by replacing the coefficient $$2$$ with the right‐hand side $$5y+7z+14$$, yielding  
$$
\left[5y+7z+14\right].
$$
This 1×1 determinant is expanded along the only row (ROW1): we simply have  
$$
D_x = 5y+7z+14.
$$

Step 4. Now, applying Cramer’s rule, we obtain  
$$
x = \frac{D_x}{D} = \frac{5y+7z+14}{2}.
$$

Thus, the solution for $$x$$ is  
$$
x = \frac{5y+7z+14}{2}.
$$
$$ x = \frac{5y + 7z + 14}{2} $$

[

2 x-7 z=5 y+14

]

Solve for only using Crammer’s rule. Expand along ROW1 only.
(10)

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[ 2 x-7 z=5 y+14 ] Solve for only using Crammer’s rule. Expand along ROW1 only. (10)