This document summarizes three methods for solving systems of linear equations with two unknowns: 1) The method of substitution substitutes the equation into the other. 2) The method of elimination eliminates one variable by adding a multiple of one equation to the other. 3) An example problem is worked out using the three methods.

1. Sistema de ecuación lineal
ALUMNA: ALEXANDRA GUTIERREZ DENOS
ESPECIALIDAD: MATEMATUCA III

2.  SISTEMA DE ECUACIONES CON DOS
INCOGNITAS
 METODO DE IGUALACION
2𝑥 + 𝑦 = 8
3𝑥 − 2𝑦 = 5
a
b
a) 2𝑥 + 𝑦 = 8
2𝑥 = 8 − 𝑦
𝑥 =
8 − 𝑦
2
b) 3𝑥 − 2𝑦 = 5
3𝑥 = 5 + 2𝑦
𝑥 =
5 + 2𝑦
3
8 − 𝑦
2
=
5 + 2𝑦
3
24 − 3𝑦
= 10 + 4𝑦
24 − 10 = 7𝑦
14
7
= 𝑦
𝟐 = 𝒚
𝑥 =
8 − 𝑦
2
𝑥 =
8 − 2
2
𝒙 = 𝟑

3. METODO DE SUSTITUCION
3𝑥 + 5𝑦 = 3
2𝑥 + 3𝑦 = 1
a
b
a) 3𝑥 + 5𝑦 = 3
3𝑥 = 3 − 5𝑦
𝑥 =
𝟑 − 𝟓𝒚
𝟑
b) 2𝒙 + 3𝑦 = 1
2
𝟑−𝟓𝐲
𝟑
+ 3𝑦 = 1
2 3 − 5𝑦 + 9𝑦 = 3
6 − 10𝑦 + 9𝑦 = 3
6 − 𝑦 = 3
−𝑦 = 3 − 6
𝑦 = 𝟑
𝑥 =
3−5𝑦
3
=
3−5(3)
3
= −4

4. METODO DE REDUCCION
5𝑥 − 𝑦 = 6
𝑥 + 3𝑦 = 10
(3)
15𝑥 − 3𝑦 = 18
𝑥 + 3𝑦 = 10
16𝑥 = 18
𝑥 =
18
16
𝑥 =
7
4
𝑥 + 3𝑦 = 10
7
4
+ 3𝑦 = 10
7
4
− 10 = −3𝑦
33
4
/3 = 𝑦
11
4
= 𝑦

5. EJERCICIOS
𝟑𝑿 + 𝟐𝒀 = 𝟔

𝑿 + 𝒀 = 𝟗
𝟓𝒀 − 𝒀 = 𝟒