Answer:
130
Explanation:
We are given the following system of equations

From this system, we can create the following coefficient matrix
![\left[\begin{array}{ccc}4&3&2\\-3&1&5\\-1&-4&3\end{array}\right]](https://img.qammunity.org/2021/formulas/mathematics/middle-school/23t4gdqglcqquw231b7vo28ut0zj4ppj3h.png)
Let us go over a method of finding the determinant of a 3x3 matrix real quick.
![\left[\begin{array}{ccc}a&b&c\\d&e&f\\h&i&j\end{array}\right]](https://img.qammunity.org/2021/formulas/mathematics/middle-school/7voan2q9suik6w24dihw0u1wqbny86009z.png)
If this is our 3x3 matrix, the determinant will be as follows
![a*det(\left[\begin{array}{ccc}e&f\\i&j\\\end{array}\right]) -b*det(\left[\begin{array}{ccc}d&f\\h&j\\\end{array}\right]) +c*det(\left[\begin{array}{ccc}d&e\\h&i\\\end{array}\right] )](https://img.qammunity.org/2021/formulas/mathematics/middle-school/oqea8kg1n3fgklgprv3rtji0bc9j40kins.png)
Which is the same thing as

Now back to our original system
![\left[\begin{array}{ccc}4&3&2\\-3&1&5\\-1&-4&3\end{array}\right]](https://img.qammunity.org/2021/formulas/mathematics/middle-school/23t4gdqglcqquw231b7vo28ut0zj4ppj3h.png)
Using this same formula, we can find the determinant
![4*([1*3]-[-4*5])-3([-3*3]-[-1*5])+2([-3*(-4)]-[-1*1])\\\\4(3+20)-3(-9+5)+2(12+1)\\\\4(23)-3(-4)+2(13)\\\\92+12+26=130](https://img.qammunity.org/2021/formulas/mathematics/middle-school/obv4a42b5erwi5r5iogwv4aursvezreua6.png)