Question

or
Solve this system of equations by graphing. First graph the equations, and then type the solution.
y=
–
6x
y=
–
7x–1
Click to select points on the graph.

Answer 1

To solve the system of equations by graphing, we have the following equations to work with:

1. \( y = -6x \)
2. \( y = -7x - 1 \)

### Step 1: Graph the equations

**Graph of the first equation \( y = -6x \)**:
- The slope is -6 and the y-intercept is 0.
- Plot two points:
- When \( x = 0 \), \( y = 0 \) (the y-intercept).
- When \( x = 1 \), \( y = -6 \) (point (1, -6)).
- Draw a straight line through these points.

**Graph of the second equation \( y = -7x - 1 \)**:
- The slope is -7 and the y-intercept is -1.
- Plot two points:
- When \( x = 0 \), \( y = -1 \) (the y-intercept).
- When \( x = 1 \), \( y = -8 \) (point (1, -8)).
- Draw a straight line through these points.

### Step 2: Find the intersection point

Once you have the lines graphed, you look for the point where they intersect.

### Finding the Solution Algebraically

To find the solution numerically (for confirmation), set the equations equal to each other:

\[
-6x = -7x - 1
\]

Now solve for \( x \):

\[
-6x + 7x = -1
\]
\[
x = -1
\]

Now substitute \( x = -1 \) back into either equation to find \( y \):

Using the first equation:
\[
y = -6(-1) = 6
\]

### Solution

The solution (intersection point) is:
\[
(x, y) = (-1, 6)
\]

So, the solution to the system of equations is:

\[
\boxed{(-1, 6)}
\]