Question

y = 3x + 6, y = -13x - 4

Answer 1

To solve the system of equations given by \( y = 3x + 6 \) and \( y = -13x - 4 \), we can set the two equations equal to each other since both are equal to \( y \):

\[
3x + 6 = -13x - 4
\]

Now, we can solve for \( x \):

1. Add \( 13x \) to both sides:

\[
3x + 13x + 6 = -4
\]
\[
16x + 6 = -4
\]

2. Subtract 6 from both sides:

\[
16x = -4 - 6
\]
\[
16x = -10
\]

3. Divide both sides by 16:

\[
x = -\frac{10}{16} = -\frac{5}{8}
\]

Now that we have \( x = -\frac{5}{8} \), we can substitute this value back into one of the original equations to find \( y \). We'll use the first equation \( y = 3x + 6 \):

\[
y = 3\left(-\frac{5}{8}\right) + 6
\]
\[
y = -\frac{15}{8} + 6
\]
Convert 6 to a fraction with a denominator of 8:

\[
y = -\frac{15}{8} + \frac{48}{8} = \frac{33}{8}
\]

So the solution to the system of equations is:

\[
\left( -\frac{5}{8}, \frac{33}{8} \right)
\]

This is the point where the two lines intersect.