Solve the following system of equations graphically on the set of axes below. y = -1/6 x - 1; x - y = 8.
Understand the Problem
The question is asking us to solve a system of equations by plotting two lines on a graph. The user will need to find the points where the lines intersect to determine the solution to the system.
Answer
The solution is the point $ (2, -6) $.
Answer for screen readers
The solution to the system of equations occurs at the intersection point, which can be found at $ (2, -6) $.
Steps to Solve
- Identify the equations The given equations are $$ y = -\frac{1}{6}x - 1 $$ and $$ x - y = 8 $$.
Rearranging the second equation gives: $$ y = x - 8 $$.
- Plot the first line To plot the line represented by the equation $$ y = -\frac{1}{6}x - 1 $$, identify two points.
- When $x = 0$: $$ y = -1 $$ (0, -1)
- When $x = 6$: $$ y = -2 $$ (6, -2)
Plot these points and draw the line passing through them.
- Plot the second line For the second line $$ y = x - 8 $$, find two points.
- When $x = 0$: $$ y = -8 $$ (0, -8)
- When $x = 8$: $$ y = 0 $$ (8, 0)
Plot these points and draw the line passing through them.
- Find the intersection Look for the point where the two lines intersect on the graph. This point represents the solution to the system of equations.
The solution to the system of equations occurs at the intersection point, which can be found at $ (2, -6) $.
More Information
The intersection point represents the values of $x$ and $y$ that satisfy both equations simultaneously. Graphical solutions provide a visual understanding of how equations interact, making it a helpful method in algebra.
Tips
- Not accurately plotting points, which can lead to a wrong intersection point.
- Confusing the direction of the lines when using negative slopes.
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