Question

Solve the system of equations graphed .
y = -1/2x - 5. y = 3x + 2
(−4,−2) open paren negative 4 comma negative 2 close paren (−2,−4) open paren negative 2 comma negative 4 close paren (−5,2) open paren negative 5 comma 2 close paren (0,−5) open paren 0 comma negative 5 close paren Skip to navigation

Answer 1

To solve the system of equations given by:

1. \( y = -\frac{1}{2}x - 5 \)
2. \( y = 3x + 2 \)

We will set the two equations equal to each other to find the point of intersection:

\[
-\frac{1}{2}x - 5 = 3x + 2
\]

To eliminate the fraction, we can multiply the entire equation by 2:

\[
-1x - 10 = 6x + 4
\]

Next, we combine like terms:

\[
-1x - 6x = 4 + 10
\]
\[
-7x = 14
\]

Dividing both sides by -7:

\[
x = -2
\]

Now that we have \( x = -2 \), we can substitute this value back into either of the original equations to find \( y \). Let's use the second equation:

\[
y = 3(-2) + 2
\]
\[
y = -6 + 2 = -4
\]

Thus, the point of intersection, or the solution to the system of equations, is:

\[
(-2, -4)
\]

The correct answer from the provided options is:

**(−2,−4)**.