Question

3.steps for solving a system of linear equations by graphing
step 1
step 2
step 3
using the 3 steps
solve the system by graphing.
\\(\

$$\begin{cases} y = -3x - 8 \\\\ y = \\frac{1}{2}x - 1 \\end{cases}$$

\\)

Explanation:

Step 1: Graph the first line \( y = -3x - 8 \)

To graph \( y = -3x - 8 \), we can find two points.

• When \( x = 0 \), \( y = -3(0) - 8 = -8 \), so we have the point \( (0, -8) \).
• When \( x = -2 \), \( y = -3(-2) - 8 = 6 - 8 = -2 \), so we have the point \( (-2, -2) \).

Plot these two points and draw a line through them.

Step 2: Graph the second line \( y = \frac{1}{2}x - 1 \)

To graph \( y = \frac{1}{2}x - 1 \), we find two points.

• When \( x = 0 \), \( y = \frac{1}{2}(0) - 1 = -1 \), so we have the point \( (0, -1) \).
• When \( x = 2 \), \( y = \frac{1}{2}(2) - 1 = 1 - 1 = 0 \), so we have the point \( (2, 0) \).

Plot these two points and draw a line through them.

Step 3: Find the intersection point

The two lines intersect at the point where their \( x \) and \( y \) values are equal. By looking at the graph (or solving the system algebraically: set \( -3x - 8=\frac{1}{2}x - 1 \), then \( -3x-\frac{1}{2}x=-1 + 8 \), \( -\frac{7}{2}x = 7 \), \( x=-2 \), and substituting \( x = -2 \) into \( y=-3x - 8 \) gives \( y=-3(-2)-8 = 6 - 8=-2 \)), the intersection point is \( (-2, -2) \).

Step 4: Check the solution

Substitute \( x=-2 \) and \( y = -2 \) into both equations:

• For \( y=-3x - 8 \): \( -2=-3(-2)-8=6 - 8=-2 \) (true).
• For \( y=\frac{1}{2}x - 1 \): \( -2=\frac{1}{2}(-2)-1=-1 - 1=-2 \) (true).

Answer:

The solution to the system is \( x=-2 \), \( y = -2 \) or the ordered pair \( (-2, -2) \).