Question

enter values for a and b so that the systems of equations has one solution -y=-6x-4 and y=ax+b

Answer 1

To determine values for \( a \) and \( b \) so that the system of equations has one solution, the equations must represent two lines that intersect at exactly one point.

The first equation is given as:

\[
-y = -6x - 4
\]

We can rewrite this in slope-intercept form \( y = mx + c \):

\[
y = 6x + 4
\]

This means the slope \( m_1 \) of the first line is \( 6 \).

The second equation is given as:

\[
y = ax + b
\]

For the system to have one solution, the slope \( m_2 \) of this line must be different from \( m_1 \). Thus, we need:

\[
a \neq 6
\]

The value of \( b \) can be any real number.

Here are some example values for \( a \) and \( b \) that satisfy these conditions:

1. \( a = 5 \), \( b = 0 \)
2. \( a = 7 \), \( b = 2 \)
3. \( a = -1 \), \( b = 3 \)

As long as \( a \) is not equal to \( 6 \), you can choose any value for \( b \) to ensure the system has one solution.