The document solves a system of 3 equations with variables x, y, and z. It finds the determinants of the coefficients matrix and the matrices from each equation (Δ1, Δ2, Δ3) and the overall determinant (Δ). It uses Cramer's rule to calculate the values of x, y, and z by taking the ratio of the determinants from each equation to the overall determinant, resulting in x=-2, y=5, z=7.

1. Resolver las 3 ecuaciones
𝑥 − 3𝑦 + 2𝑧 = −3
5𝑥 + 6𝑦 − 𝑧 = 13
4𝑥 − 𝑦 + 3𝑧 = 8
1 − 3 + 2 ⋮ −3
5 + 6 − 1 ⋮ 13
4 − 1 + 3 ⋮ 8
1 −3 2
5 6 −1
4 −1 3
−3
13
8
𝒙 =
∆𝟏
∆
𝒚 =
∆𝟐
∆
𝒛 =
∆𝟑
∆
1
5
4
−3
6
−1
2
−1
3
1
5
4
−3
6
−1
[ 18 + 12 + −10 ] − [ 48 + 1 + −45 ]
[ 20 ] − 4 = 20 − 4 = 𝟏𝟔
Encontrar Δ
−3
13
8
−3
6
−1
2
−1
3
−3
13
8
−3
6
−1
[ −54 + 24 + −26 ] − [ 96 + −3 + −117 ]
[ −56 ]− −24 = −56 + 24 = −𝟑𝟐
Encontrar Δ1

2. 1 −3 2
5 6 −1
4 −1 3
−3
13
8
𝒙 =
∆𝟏
∆
𝒚 =
∆𝟐
∆
𝒛 =
∆𝟑
∆
1
5
4
−3
13
8
2
−1
3
1
5
4
−3
13
8
[ 39 + 12 + 80 ] − [ 104 + −8 + −45 ]
[ 131 ]− 51 = 131 − 51 = 𝟖𝟎
Encontrar Δ2
1
5
4
−3
6
−1
−3
13
8
1
5
4
−3
6
−1
[ 48 + −156 + 15 ] − [ −72 + −13 + −120 ]
[ −93 ] − −205 = −93 + 205 = 𝟏𝟏𝟐
Encontrar Δ3

3. 𝒙 =
−𝟑𝟐
𝟏𝟔
= −𝟐
𝒚 =
𝟖𝟎
𝟏𝟔
= 𝟓
𝒛 =
𝟏𝟏𝟐
𝟏𝟔
= 𝟕
∆ = 16
∆1 = −32
∆2 = 80
∆3 = 112
𝑥 =
∆1
∆
𝑦 =
∆2
∆
𝑧 =
∆3
∆