Question

y = –7x − 4
y = –4x + 2

Answer 1

To solve the system of equations given by:

1. \( y = -7x - 4 \)
2. \( y = -4x + 2 \)

we can find the intersection point by setting the right-hand sides of the equations equal to each other:

\[
-7x - 4 = -4x + 2
\]

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

1. Add \( 4x \) to both sides:

\[
-7x + 4x - 4 = 2
\]
\[
-3x - 4 = 2
\]

2. Now, add \( 4 \) to both sides:

\[
-3x = 2 + 4
\]
\[
-3x = 6
\]

3. Divide both sides by \( -3 \):

\[
x = -2
\]

Now that we have \( x \), we can substitute it back into one of the original equations to find \( y \). We'll use the second equation:

\[
y = -4(-2) + 2
\]
\[
y = 8 + 2
\]
\[
y = 10
\]

Thus, the solution to the system of equations is:

\[
(x, y) = (-2, 10)
\]

So the point of intersection is \((-2, 10)\).