Question

Solve the following system of equations for z and for y
:
System of Equations:

Value of z

Value of y
y=9+3z

y=58−4z

Answer 1

To solve the system of equations for \( z \) and \( y \), we can start with the two equations given:

1. \( y = 9 + 3z \)
2. \( y = 58 - 4z \)

Since both expressions equal \( y \), we can set them equal to each other:

\[
9 + 3z = 58 - 4z
\]

Next, we will solve for \( z \). First, we can add \( 4z \) to both sides:

\[
9 + 3z + 4z = 58
\]

This simplifies to:

\[
9 + 7z = 58
\]

Now, subtract 9 from both sides:

\[
7z = 49
\]

Next, divide both sides by 7:

\[
z = 7
\]

Now that we have the value for \( z \), we can substitute it back into either of the original equations to find the value of \( y \). We'll use the first equation:

\[
y = 9 + 3z
\]

Substituting \( z = 7 \):

\[
y = 9 + 3(7)
\]

Calculating it:

\[
y = 9 + 21
\]
\[
y = 30
\]

So, the solutions are:
\[
z = 7
\]
\[
y = 30
\]