Question

Solve by Graphing.

What is the solution to the system of equation?
y=-2x-6
x=-7


Question 6 options:

(1, -7)


Infinite Solutions


(-7, 8)


No Solutions

Answer 1

To solve the system of equations by graphing, we'll analyze the given equations:

1. \( y = -2x - 6 \) (This is a linear equation in slope-intercept form.)
2. \( x = -7 \) (This is a vertical line where x is always -7.)

**Step 1: Graph the first equation: \( y = -2x - 6 \)**

The y-intercept is -6, so the graph starts at the point (0, -6).

Next, since the slope is -2, we can go down 2 units and to the right 1 unit to find another point. This gives us the point (1, -8). We can plot a few points:

- When \( x = 0 \): \( y = -6 \) → Point (0, -6)
- When \( x = 1 \): \( y = -2(1) - 6 = -8 \) → Point (1, -8)
- When \( x = -1 \): \( y = -2(-1) - 6 = -4 \) → Point (-1, -4)

**Step 2: Graph the second equation: \( x = -7 \)**

This is a straight vertical line that intersects the x-axis at -7.

**Step 3: Find the intersection**

To find the intersection of the two lines, substitute \( x = -7 \) into the first equation:

\[
y = -2(-7) - 6
\]
\[
y = 14 - 6
\]
\[
y = 8
\]

So the point of intersection is \((-7, 8)\).

**Conclusion**

The solution to the system of equations is \((-7, 8)\).

Thus, the correct option is:

**(-7, 8)**