Question

Solve the system of equations.
3x−4y=40

5x−5y=55
(1 poi

Answer 1

To solve the system of equations:

1. **First equation**: \( 3x - 4y = 40 \)
2. **Second equation**: \( 5x - 5y = 55 \)

We can solve this system using either substitution or elimination. For this case, we will use the elimination method.

### Step 1: Simplify the second equation
We can simplify the second equation:
\[
5x - 5y = 55
\]
Dividing the entire equation by 5 gives:
\[
x - y = 11 \quad (1)
\]

### Step 2: Express \(x\) in terms of \(y\)
From equation (1), we can express \(x\) in terms of \(y\):
\[
x = y + 11 \quad (2)
\]

### Step 3: Substitute equation (2) into the first equation
Now substitute equation (2) into the first equation:
\[
3(y + 11) - 4y = 40
\]
Expanding this:
\[
3y + 33 - 4y = 40
\]
Combining like terms:
\[
-y + 33 = 40
\]
Subtracting 33 from both sides:
\[
-y = 40 - 33
\]
\[
-y = 7
\]
Multiplying by -1 gives:
\[
y = -7
\]

### Step 4: Substitute \(y\) back to find \(x\)
Now substitute \(y = -7\) back into equation (2):
\[
x = -7 + 11 = 4
\]

### Conclusion
The solution to the system of equations is:
\[
\boxed{(4, -7)}
\]

### Verification
We can verify by plugging \(x = 4\) and \(y = -7\) back into the original equations:

1. **Check the first equation**:
\[
3(4) - 4(-7) = 12 + 28 = 40 \quad \text{(True)}
\]

2. **Check the second equation**:
\[
5(4) - 5(-7) = 20 + 35 = 55 \quad \text{(True)}
\]

Both equations are satisfied, confirming that the solution is correct: \( \boxed{(4, -7)} \).