Question

-2y=c
7x+9y=-45
Solve by substitution

Answer 1

To solve the system of equations using substitution, we can start with the first equation, \(-2y = c\), and solve for \(y\):

1. **Solve for \(y\)**:
\[
y = -\frac{c}{2}
\]

2. **Substitute \(y\) in the second equation**:
Now we substitute \(-\frac{c}{2}\) for \(y\) in the second equation:
\[
7x + 9y = -45
\]
becomes
\[
7x + 9\left(-\frac{c}{2}\right) = -45
\]

3. **Simplify the equation**:
\[
7x - \frac{9c}{2} = -45
\]

4. **Isolate \(x\)**:
Let's first move \(-\frac{9c}{2}\) to the right side:
\[
7x = -45 + \frac{9c}{2}
\]
Now, divide by 7 to solve for \(x\):
\[
x = \frac{-45 + \frac{9c}{2}}{7}
\]

So, we have:
\[
x = \frac{-45 + \frac{9c}{2}}{7}
\]
and
\[
y = -\frac{c}{2}
\]

This gives us the values of \(x\) and \(y\) in terms of \(c\):
\[
x = \frac{-90 + 9c}{14}
\]
\[
y = -\frac{c}{2}
\]

These expressions represent the solution to the system in terms of \(c\). If you have a specific value for \(c\), you can substitute it to find the numerical values of \(x\) and \(y\).