solve system of equations 5x-4y=-45 and 3x=2y-27

To solve the system of equations:

\[
\begin{aligned}
1. & \quad 5x - 4y = -45 \\
2. & \quad 3x = 2y - 27
\end{aligned}
\]

we can use either substitution or elimination. Let's use the substitution method for this solution.

### Step 1: Solve the second equation for \( x \):

Starting with the second equation:

\[
3x = 2y - 27
\]

Divide both sides by 3 to solve for \( x \):

\[
x = \frac{2y - 27}{3}
\]

### Step 2: Substitute this expression for \( x \) into the first equation:

Now substitute \( x = \frac{2y - 27}{3} \) into the first equation:

\[
5\left(\frac{2y - 27}{3}\right) - 4y = -45
\]

### Step 3: Clear the fraction by multiplying through by 3:

\[
5(2y - 27) - 12y = -135
\]

Distribute the 5:

\[
10y - 135 - 12y = -135
\]

### Step 4: Combine like terms:

\[
-2y - 135 = -135
\]

### Step 5: Solve for \( y \):

Add 135 to both sides:

\[
-2y = 0
\]

Divide by -2:

\[
y = 0
\]

### Step 6: Substitute \( y = 0 \) back into the expression for \( x \):

Substitute \( y = 0 \) into \( x = \frac{2y - 27}{3} \):

\[
x = \frac{2(0) - 27}{3} = \frac{-27}{3} = -9
\]

### Solution:

The solution to the system of equations is:

\[
x = -9, \quad y = 0
\]

Would you like further details or have any questions?

Here are 5 related questions you might consider:
1. What is the solution to the system using the elimination method?
2. How can you verify the solution by substituting the values back into the original equations?
3. What would the system look like if both equations were multiplied to clear fractions before solving?
4. How do these techniques apply to systems of three equations in three variables?
5. Can you graphically interpret the solution of the system?

**Tip:** When solving a system of linear equations, always check your solution by substituting it back into the original equations to ensure accuracy.

Learn how to solve the system of equations 5x-4y=-45 and 3x=2y-27 with detailed step-by-step instructions using the substitution method. This problem involves solving simultaneous equations using algebraic methods. Suitable for students in Grades 9-12.

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