Example 5.9 from Elementary Algebra, 5.1 Solve Systems of Equations by Graphing

Solve Systems of Equations by Graphing: example 5.9

Without graphing, determine the number of solutions and then classify the system of equations: ${\begin{matrix} y = 3 x - 1 \\ 6 x - 2 y = 12 \end{matrix} .$

Work it out on paper first. Then open the solution one step at a time, and stop as soon as you can finish on your own.

Your turn

The book's Try It right after this example: same idea, new numbers. Only the answer is given.

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

${\begin{matrix} y = - 2 x - 4 \\ 4 x + 2 y = 9 \end{matrix}$

How did it go?

We will compare the slopes and intercepts of the two lines.	${\begin{matrix} y = 3 x - 1 \\ 6 x - 2 y = 12 \end{matrix} .$
The first equation is already in slope-intercept form.	$y = 3 x - 1$
Write the second equation in slope-intercept form.	$\begin{matrix} 6 x - 2 y & = & 12 \\ −2 y & = & −6 x + 12 \\ \frac{−2 y}{−2} & = & \frac{−6 x + 12}{−2} \\ y & = & 3 x - 6 \end{matrix}$
Find the slope and intercept of each line.	$\begin{matrix} y & = & 3 x - 1 & y & = & 3 x - 6 \\ m & = & 3 & m & = & 3 \\ b & = & −1 & b & = & −6 \end{matrix}$
	Since the slopes are the same and $y$ -intercepts are different, the lines are parallel.

We will compare the slopes and intercepts of the two lines.	${\begin{matrix} y = 3 x - 1 \\ 6 x - 2 y = 12 \end{matrix} .$
The first equation is already in slope-intercept form.	$y = 3 x - 1$
Write the second equation in slope-intercept form.	$\begin{matrix} 6 x - 2 y & = & 12 \\ −2 y & = & −6 x + 12 \\ \frac{−2 y}{−2} & = & \frac{−6 x + 12}{−2} \\ y & = & 3 x - 6 \end{matrix}$
Find the slope and intercept of each line.	$\begin{matrix} y & = & 3 x - 1 & y & = & 3 x - 6 \\ m & = & 3 & m & = & 3 \\ b & = & −1 & b & = & −6 \end{matrix}$
	Since the slopes are the same and $y$ -intercepts are different, the lines are parallel.

Solve Systems of Equations by Graphing: example 5.9

Solution

Your turn

Solve Systems of Equations by Graphing: example 5.9

Solution

Your turn