Question

Solve the system of equations graphed on the coordinate axes below.
y, equals, minus, 4, x, minus, 2
y=
−4x−2
y, equals, one half, x, minus, 2
y=
2
1
​
x−2

Answer 1

To solve the system of equations given by:

1. \( y = -4x - 2 \)
2. \( y = \frac{1}{2}x - 2 \)

we can set the two equations equal to each other since they both equal \( y \):

\[
-4x - 2 = \frac{1}{2}x - 2
\]

Now, let's solve for \( x \):

1. Add 2 to both sides:

\[
-4x = \frac{1}{2}x
\]

2. To eliminate the fraction, let's multiply every term by 2:

\[
-8x = x
\]

3. Now, add \( 8x \) to both sides:

\[
0 = 9x
\]

4. Divide by 9:

\[
x = 0
\]

Now that we have \( x \), we can substitute it back into either equation to find \( y \). Using the second equation:

\[
y = \frac{1}{2}(0) - 2 = -2
\]

Thus, the solution to the system of equations is:

\[
(x, y) = (0, -2)
\]

To summarize, the solution to the system of equations is \( (0, -2) \).