Question

what solution is y= 3x + 6, y= -13x - 4

Answer 1

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

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

Now, we will 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 by 16:
\[
x = -\frac{10}{16} = -\frac{5}{8}
\]

Now that we have \( x \), we can substitute it back into either equation to find \( y \). We will use the first equation \( y = 3x + 6 \):

\[
y = 3\left(-\frac{5}{8}\right) + 6
\]
\[
y = -\frac{15}{8} + 6
\]
\[
y = -\frac{15}{8} + \frac{48}{8}
\]
\[
y = \frac{48 - 15}{8} = \frac{33}{8}
\]

So the solution to the system of equations is:

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