Chapter

Chapter 1
Section

Lectures and Quick Notes(1.2

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Lectures
4 Videos

- Linear systems mean there are 2 or more equations, but typically 2, where there are more than 1 unknown.

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Section Intro

*ex* From `6a + 5b = 12`

, isolate the variable `a`

.

Therefore, `a = 2 - \dfrac{5}{6}b`

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Isolating Variable when there are Two

**Substitution method ex1**

Solve for `(x, y)`

when

```
\displaystyle
\begin{cases}
x + y = 3 \\
2x - y = -1
\end{cases}
```

**solution**

```
\displaystyle
(x, y) = (\frac{2}{3}, \frac{7}{3})
```

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2.47mins

Substitution method ex1

**Substitution method ex2**

Solve for `(x, y)`

when

```
\displaystyle
\begin{cases}
3x + 10y = 12 \\
2x - 7y = 2
\end{cases}
```

**solution**

```
\displaystyle
(x, y) = (\frac{104}{41}, \frac{18}{41})
```

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4.37mins

Substitution method ex2