Example 5.10 from Elementary Algebra, 5.1 Solve Systems of Equations by Graphing

Solve Systems of Equations by Graphing: example 5.10

Without graphing, determine the number of solutions and then classify the system of equations: ${\begin{matrix} 2 x + y = - 3 \\ x - 5 y = 5 \end{matrix} .$

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.

${\begin{matrix} 3 x + 2 y = 2 \\ 2 x + y = 1 \end{matrix}$

How did it go?

We will compare the slope and intercepts of the two lines.	${\begin{matrix} 2 x + y = - 3 \\ x - 5 y = 5 \end{matrix}$
Write both equations in slope-intercept form.	$\begin{matrix} 2 x + y & = & −3 \\ y & = & −2 x −3 \end{matrix}$	$\begin{matrix} x - 5 y = 5 & = & 5 \\ −5 y & = & − x + 5 \\ \frac{−5 y}{−5} & = & \frac{− x + 5}{−5} \\ y & = & \frac{1}{5} x - 1 \end{matrix}$
Find the slope and intercept of each line.	$\begin{matrix} y & = & −2 x - 3 \\ m & = & −2 \\ b & = & −3 \end{matrix}$	$\begin{matrix} y & = & \frac{1}{5} x - 1 \\ m & = & \frac{1}{5} \\ b & = & −1 \end{matrix}$
	Since the slopes are different, the lines intersect.

We will compare the slope and intercepts of the two lines.	${\begin{matrix} 2 x + y = - 3 \\ x - 5 y = 5 \end{matrix}$
Write both equations in slope-intercept form.	$\begin{matrix} 2 x + y & = & −3 \\ y & = & −2 x −3 \end{matrix}$	$\begin{matrix} x - 5 y = 5 & = & 5 \\ −5 y & = & − x + 5 \\ \frac{−5 y}{−5} & = & \frac{− x + 5}{−5} \\ y & = & \frac{1}{5} x - 1 \end{matrix}$
Find the slope and intercept of each line.	$\begin{matrix} y & = & −2 x - 3 \\ m & = & −2 \\ b & = & −3 \end{matrix}$	$\begin{matrix} y & = & \frac{1}{5} x - 1 \\ m & = & \frac{1}{5} \\ b & = & −1 \end{matrix}$
	Since the slopes are different, the lines intersect.

Solve Systems of Equations by Graphing: example 5.10

Solution

Your turn

Solve Systems of Equations by Graphing: example 5.10

Solution

Your turn