Question

x+y=9
7x+7y=b

Find the value of b so that the system has an infinite number of solutions.

Answer 1

To find the value of \( b \) such that the system of equations has an infinite number of solutions, we need to express both equations in a way that they represent the same line.

The first equation is:

\[
x + y = 9
\]

We can solve this for \( y \):

\[
y = 9 - x
\]

Now, let’s rewrite the second equation:

\[
7x + 7y = b
\]

We can factor out the 7:

\[
7(x + y) = b
\]

Substituting \( x + y \) from the first equation into the second equation gives:

\[
7(9) = b
\]

Calculating that:

\[
b = 63
\]

Thus, for the system to have an infinite number of solutions, the value of \( b \) should be

\[
\boxed{63}
\]