Question

Solve by Graphing.

What is the solution to the system of equation?


{y=-2x-6
{x=-7
Question 10 options:

No Solutions


(1, -7)


Infinite Solutions


(-7, 8)

Answer 1

To solve the system of equations by graphing, we can analyze both equations:

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

**Graphing the first equation \( y = -2x - 6 \)**:
- This is a linear equation with a slope of -2 and a y-intercept of -6.
- We can find another point by substituting a value for \( x \):
- If \( x = 0 \):
\[
y = -2(0) - 6 = -6 \quad \text{(Point: (0, -6))}
\]
- If \( x = 1 \):
\[
y = -2(1) - 6 = -8 \quad \text{(Point: (1, -8))}
\]

**Graphing the second equation \( x = -7 \)**:
- This is a vertical line that passes through \( x = -7 \) for all values of \( y \).

**Finding the intersection**:
- To find the intersection of the two equations, we can substitute \( x = -7 \) into the first equation:
\[
y = -2(-7) - 6 = 14 - 6 = 8
\]
- So, the point where the two lines intersect is \( (-7, 8) \).

Thus, the solution to the system of equations is:

\[
\text{Option: } (-7, 8)
\]