Exemplo 5.11 de Elementary Algebra, 5.1 Solve Systems of Equations by Graphing

Solve Systems of Equations by Graphing: exemplo 5.11

Problema e solução em inglês, como no livro original.

Without graphing, determine the number of solutions and then classify the system of equations. ${\begin{matrix} 3 x - 2 y = 4 \\ y = \frac{3}{2} x - 2 \end{matrix}$

Resolva no papel primeiro. Depois abra a solução um passo de cada vez e pare assim que conseguir terminar sozinho.

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Without graphing, determine the number of solutions and then classify the system of equations.

${\begin{matrix} 4 x - 5 y = 20 \\ y = \frac{4}{5} x - 4 \end{matrix}$

Como foi?

We will compare the slopes and intercepts of the two lines.	${\begin{matrix} 3 x - 2 y = 4 \\ y = \frac{3}{2} x - 2 \end{matrix}$
Write the first equation in slope-intercept form.	$\begin{matrix} 3 x - 2 y & = & 4 \\ −2 y & = & −3 x + 4 \\ \frac{−2 y}{−2} & = & \frac{−3 x + 4}{−2} \\ y & = & \frac{3}{2} x - 2 \end{matrix}$
The second equation is already in slope-intercept form.	$\begin{matrix} y = \frac{3}{2} x - 2 \end{matrix}$
	Since the slopes are the same, they have the same slope and same $y$ -intercept and so the lines are coincident.

We will compare the slopes and intercepts of the two lines.	${\begin{matrix} 3 x - 2 y = 4 \\ y = \frac{3}{2} x - 2 \end{matrix}$
Write the first equation in slope-intercept form.	$\begin{matrix} 3 x - 2 y & = & 4 \\ −2 y & = & −3 x + 4 \\ \frac{−2 y}{−2} & = & \frac{−3 x + 4}{−2} \\ y & = & \frac{3}{2} x - 2 \end{matrix}$
The second equation is already in slope-intercept form.	$\begin{matrix} y = \frac{3}{2} x - 2 \end{matrix}$
	Since the slopes are the same, they have the same slope and same $y$ -intercept and so the lines are coincident.

Solve Systems of Equations by Graphing: exemplo 5.11

Solução

Sua vez

Solve Systems of Equations by Graphing: exemplo 5.11

Solução

Sua vez