To solve the system of equations by graphing, you'll need to follow these steps:
1. Understand the Equations:
[tex]\[
\begin{array}{l}
y = -\frac{3}{5} x - 1 \\
y = -\frac{4}{5} x
\end{array}
\][/tex]
2. Graph the First Equation ([tex]\( y = -\frac{3}{5} x - 1 \)[/tex]):
- This is a linear equation with slope [tex]\( -\frac{3}{5} \)[/tex] and y-intercept [tex]\( -1 \)[/tex].
- To graph this, start by plotting the y-intercept at the point (0, -1).
- From the y-intercept, use the slope to find another point. A slope of [tex]\( -\frac{3}{5} \)[/tex] means that for every 5 units you move to the right, you move 3 units down.
- So, from (0, -1), move 5 units to the right to (5, -1), and then 3 units down to (5, -4).
- Plot these points and draw the line through them.
3. Graph the Second Equation ([tex]\( y = -\frac{4}{5} x \)[/tex]):
- This is another linear equation with slope [tex]\( -\frac{4}{5} \)[/tex] and y-intercept at 0 (because there is no constant added to this equation).
- Start by plotting the y-intercept at the point (0, 0).
- From the y-intercept, use the slope to find another point. A slope of [tex]\( -\frac{4}{5} \)[/tex] means that for every 5 units you move to the right, you move 4 units down.
- So, from (0, 0), move 5 units to the right to (5, 0), and then 4 units down to (5, -4).
- Plot these points and draw the line through them.
4. Find the Intersection:
- Now that you have both lines plotted, the solution to the system of equations is the point where these two lines intersect.
- Observing the graph, you'll see that the lines intersect at the point (5, -4).
5. Conclusion:
- The solution to the system of equations is the point where the two lines meet. Thus, the solution is:
[tex]\[
(5, -4)
\][/tex]
This means the values of [tex]\( x \)[/tex] and [tex]\( y \)[/tex] that satisfy both equations simultaneously are [tex]\( x = 5 \)[/tex] and [tex]\( y = -4 \)[/tex].
